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0.1 Abstract

The objective of the three essay s of this doctoral dissertation is to investigate the strategic

choies of organizational hrms by competing &ms in vatious environments.

The kst essay, which is a pint work with PmPessor Guofu Tan, provides an alternative

theory of divestitnres that relies on product-line oomplementarities and product market

competition. We consida a simple environment in which there are two firme, each sup-

piyiiig a goup of ampiementary products and the products auoss poups are impexkct

substitutes. We mode1 the firms' choices of divesting and pricing as a two-stage game.

The duopolists simultang>nsly choose th& divestitnre strate@ in the first stage of the

game and the independent divisions compete by setting prices in the second. It is shonn

that, when competing with each other, finne with complemeutaty product-lines have in-

centives to ql i t into multiple independent divisions supplping complementary products

and setvices. Soch divestitures increase prices and the parent firms' values but reduce

aggregate social welfare. Moraver, the degree of divestitare, as ne illustrate in the lin-

e u demand case, depends on the severity of competition and the nature of product-Iines.

Then, intensified competition due to deregdafion, trade liberalization and entry may trig-

ger divestitures. We further show that if two f h aie able to mordhate th& divestitnre

strate*, they can achieve the pint monopoly pries and profits in a non-ooopaative

price game.

The second essay analyzes the strategic incentive of oligopolists to create autonomous

rival divisions when ptoducts are ditferentiated. We consider a two stage game where firms

choose the number of autonomous divisions in the first stage a d al1 the divisions engage

in Cournot competition in the second. It is shown that product difkentiation enmes the

existence of an interior wbgame pe&d Nash eqnilibrium, and the eqnilibri~m number

of divisions inmeases with the degree of substitution among produds aad the numba

of h s . Wher, if divisions are allowed to hirther divide, they always wiJl, which

leads to total tent dissipation. Thus, parent firms have incentives to anilaterdy restrict

theh divisions kom further dividing. Li the & entry eqnilibrium, it is hund that the

possibility of setting ap autonornons dmeione is a natual b& to d r y . Liaunbente

may persiste& eam abnomially high profits. In the cases where product Mkentiation

is difficult, the only pure strategy free entry eqpilibrium is the monopoly outcome even if

the entry cost is relatively low . The third essay dwelops a game themetic model to analyze strategic leasing behaviots

of loadownem in a nonexdusively owned common oil pool. The oü fidd deveiopment is

modeled as two moreor-less independent onestage noncooperative game. The laadown-

ers choose leasing strategies in the h s t stage, and independent le- operators cbooae

extraction strategies in the second. It is hund that, in a nonexclusively owned oil field, it

is individually rational for a landorner to naJataally mbdivide his ladholding and dele-

gate production rights to multiple independent firms, even though more dispersed produc-

tion control leads to heavier cornmon pool losses. Moieover, the degree of laudownership

concentration detemines the degree of production conmtration. The more hsgmented

the laad ownership, the lower is the degree of production concentration in equilibrium.

The analysis offers an expianation for the piiazling landomed leasing behaviors in U.S.

onshore oil fields.

Contents

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.1 Abstract ii

. . . . . . . . . . . . . . . . . . . . . . . . . . . . * . 0.2 Acknowledgment . . v;

1 Introduction 1

2 Compiements. Substitutes and Strategic Diveditute 7

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Introduction 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 The Mode1 12

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Andyais 15

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 TwoBenchmarks 15

. . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Second-Stage Price Game 18

. . . . . . . . . . . . . . . . . . . . . 2.3.3 Strategic hcentives to Divest 21

. . . . . . . . . . . . . . . . . . . . . . . . 2.3.4 Coordinated divestitures 25

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Extensions 28

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Con&dingR,em arks 30

3 Product Differentiation. Strategic Divisionabation and Persistence of

Monopoly 33

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Introduction 33

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 The Modd 36

. . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Demand and Technology 36

. . . . . . . . . . . . . . . . . . . . . . 3.23 The Divisionalization Game 37

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Andysis 38

. . . . . . . . . . . . . . 31.1 The Second Stage Cournot Qnantity Giune 38

. . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 The First Stage Game 40

. . . . . . . . . . . . . . . . . . . . 3.4 Possibility of Fnrther Divisio~aiization 44

4 Divide and Conquer: Strategic Leasing in Common Pool Oil Fields 61

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Introduction 51

. . . . . . . . . . . . . . . . 4.2 Oil Extraction Technology in a Cornmon Pool 54

. . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 The Ektraction Rate 54

. . . . . . . . . . . . . . . . . . . 4.2.2 The Pressnre Depletion Dynamics 55

. . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 The Ultimate Recovery 56

. . . . . . . . . . . . . . . . . . . . 4.3 Andysis of Cornpetitive Oü Extraction 57

. . . . . 4.4 A Game Thmetic Mode1 of Strakgic Leasing in a Common Pool 60

4.4.1 The Potential Gain of a Multiple Leasing Strategy: An Example . . 61 . . . . . . . . . . . . . . . . . . . . . 4.4.2 Analgsis of the Leasing Game 63

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Conclusion 65

5 Conclusion 67

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Appendix2.A 77

. . . . . . . . . . . . . . 5.2 Appendix 2.B. An Integer Divisionalization Game 80 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Appendir 3 84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Appendix 4.1 88

5.5 Appendix4.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

0.2 Acknowledgment

1 wodd iike to thank m y the& cornmittee, Kenneth Henàricks, Margaret Slade and especidy Guoh Taa for induable a>mments and guidance. 1 am indebted to my M y ,

e s p e d y my lovely riEe Jeany Chen and son Alexander for th& support.

Chapter 1

Introduction

The modem economy is dominated by large corporations with sophisticated structures.

Indead of being centtalized to a single entitp, production and marketing decisions in a

firm are often made by varioas levels of management, subsidiasies, divisions, &anchises,

etc.. The institutional arrangement and decision stractare in fitms are aitical factors

for economic performance. The objective of this dissertation is to investigate how firms

sttategidy set ap autonomous units when faQng cornpetition in several simplified envi-

ronments.

Coase is among the pioneers who first r e k d the importance of the study of the

"institutional strncture of production." S tirnulateci by the great debate of the advant ages

of a kee market system over a central planni~g system in the early thirties, Coase started

to rationahe the v q existence of the firm in the kee market ewnomy. Acmrding to eco-

nomic theory, a competitive market economic system coordinated by prices would deliver

the Paseto-efficient outcorne. Then, if the pricing system provides aJl the coordination

necessaty, why is there a need for firms whose function is to motdinate in a plPnnmg

fashion? In hie famous 1937 article &The Nature of the Firm," Coase acknowledged that

there are transaction msts of uing the price system. And, it is the avoidsaœ of these

wsts that codd explain the existence of the hm in which docation of fodors wmes

about as a r e d t of administrative deciaions. A dtm codd continue to ePet if it p&rms

its coordination fundion at a Iowa cost thui wodd be ocetirred if it were achieved by

means of market transactions and aLPo at a bwer cost than the same fnnction codd be

pdrmed by another firm.

Coase's theory convincingly justifies the emergenœ of the firm in the fiee market

ewnomy but stops short of explaining how and why a firm chooses a d a i n form of orge

nization. Williamson (1975) investigates the increased use of mdtidivisionai organization

hrm in big corporations documented by Chandler (1962). He argues that big organi-

zations inevitably enconnter monitoring ditüdties and mord hazard problems. Multi-

divisiond fbrm is an institutiond innovation arïsing to reduce monitoring costs and to

mitigate mord hazard problems by devolving operational deciaione to smaller autonomous

divisiond aaits. Along a similas line of argument, Aron (1988) shows that stock m e

ket evahation of separated units can teduce the costs of motivathtg managers. MW,

Milgrom aad Roberts (1992) ugue that since influence costs, which arise from the posd

bility of manipulation of p d r m a n œ m e m e s by poor p&rming anits, reduce a hm's

potential value, poor petfonning units should be divested. These theories based on asym-

metnc information or moral hazard problems do provide ration& h r why firms set up

mdtiple independently managed anits. The explmation, however, ia inamplede becoase

the potential extenid effects of a firm's choiœ of organhationid form on other firms in

the market are neglected.

Recently, many authors have reaüzed that thae is a stiategic aspect to the choiœ of

the organizational form by a firm. Vickers (1984), Fershtmui aad Judd (1987), Fersht-

man, Judd and Kalai (1991), and Sklivas (1987) stndy the separation of ownenihip and

control in management controlled firms in a duopolistic setting. The generic model is a

two-@od model. In the hst period, each orner provides his manager with an incentive

contract that is a lineu combination of profit and saies revenue or output; in the second

period, maaagess make production and d e s decisions hllowing th& o n interest in ei-

t h e a Conniot quantity game or a Bertrand pria game. These articlea show that the

sepration of ownersbip and management is the rationd response of ftme to oligopolistic

cornpetition. Moreover, the finns' goadsetting incentive contracts for managers are iatet-

dependent and ate typically not the direct profit rnadmhg schemes. Under Coumot

(Bertrand) mmpetition, finns' profits are lower (higher) telative to the case where there

is no separation of ownership and management.

These strategic delegation models have been helphl in explabhg the epltence of

management control fitms and the related compensation schexnes foi managers. Howevez,

by construction, these models c m not explain the widespread existence of mdtiple au-

tonomously mmaged nnits (such as divisions, tmchises, etc.) within a fi=, br each

ornier is only allowed to hire a single manager.

More recently, there has b e e ~ a growing interest in strategic dioiaion.lizstion, whieh

teks to Grmsy choiœs of multidivisiond btf118 under oîigopoiistic cornpetition. Schwartz

aad Thompson (1986) and Veendorp (1991) demonstrate that an incumbent monopoly can

forestall entry tkough setting up multiple identical autonomous divisions. They argue

that divisionalization can be used as a cornmitment device for the monopoly to produœ sn

en t ry -de tdg level of output. Corchon (1991), Pohiky (1992), Corchon and G o n z k

Meastre (1993), and Baye, Crocher and Ju (1996) consider a case of a symmetnc duopoly

with homogeneous products. The bairic mode1 is a twwt y game, where each daopolist

chooses the number of autonomous divisions in the ftst stage, and all divisions engage

in a Coumot competition in the second stage. The main result is that the duopolists

have incentives to nnilaterdly set up multiple autonomous M o n s . Such a strategy

commits a parent firm to a higher level of output, mimicking a Stackelberg-type outcome

in pnrsuing Coarnot competition (Baye, Crocker and Ju, 1996). In eqnilibrium, the profits

of mmpeting firms are lower and social welfare is higher than in the ndivisionaüzation

Case.

This dissertation is an attempt to expand the investigation of how and why firmo di-

vide production among autonomous units into several diflerent sœnarios of cornpetition.

It consists of t h e essays. The fitst essay sttadies divisionalkation of cornpethg mul-

tiproduct firms whea produblines eonsist of complementaq products or services. The

second essay deals with divisiondization of h n s with difle~entiated products. Finally,

the third essay investigates strategic leasing in mmmon pool oil production, which can

be viewed as a spead fotm of divisionabation. Without doubt, divisiondization in thhi

thesis is used in the broadest sense possible. It t e k s to f h s setting up independently

managed units in whatever forms, sach as independent leases, benchises, spinoffi, outright

sales, etc..

In the hst essay, a joint work with mg thesis sapervisor Professot Guofu Tan, ne

dmelop a theory of divisionalization (diveditutes) that telies on product-line complemen-

tarities and produd marlet cornpetition. We consider a simple environment in which each

of the mmpeting fitms supplies a goap of complementsry goods or serviœs. Division-

albation of a multi-product ficm ifi modeled as a partition of its product spaee. Hence,

diviaions of the same îum produœ pmducts that are complemaitary to each other. The

competition is modeled as a tao-stage game. Each fùxn choocles its number of divisions

in the f ~ s t stage, rad dl divisions engage in a Bertrand pice game in the second stage.

Undes a general demand, it is shonn that firms with complementary pmdact-lines have

incentives to set up multiple autonomous divisions anilaterally in competition. Prices and

firms' profits are higher and social w e k e is 10we.r relative to the caae where no division-

Plization is permitted. More interestingiy, if fimui are able to mordhate theV division$-

ization decisions in the kst stage, the snbsequent noncooperative Bertrand competition

in the second stage leads to monopoly prices and profits, as if all firrmi (or a l l divisions)

are managed by a single agent. The nnmber of divisions in a ~ymrnetic game is posi-

tively related to both the degree of competition, which is measured by the degtee of the

substitutability among the groaps of products, aad the number of groupe. Thetefore, this

aaaiysis b d d s a link between firms' business restructuring decisions or choiœs of organi-

zationai fona and the cornpetitive envitonment. Intensiîied competition that r e d t s hom

detegulation, trade liberalization or entnes may tfigger divisionalization. This may pre

vide a partid explanation for the coincidence of the increaaed ase of multidivisional fom

(induding divestitares) and the waves of deregdation and globdiaation in the developed

economies since the 1980s.

The key to these r e d t s is the two opposite d & s that the pricing of a ptoduct inflicts

on complements and subtditutes. It is known that an increase in the pria of a product hacr

a negative effect on the demand of its complaeents and a positive effect on the demand

of its substitutes. In abamce of divisionalbation, the prices of products of t ao competing

h s are too low relative to the monopoly prias, which maximize the awegate profits

of these firms. After divisionalization, independent divisions of the same firm ignore the

negative exteniality of pricing on each othet. Thus, the redting prices aad aggregate

profits r i e towards the monopoly level. The posaibility that firms can tacitly WU& in

pricing through divisionalization malres antitrust tegulation a more cornplex issue.

The second essay aaalyzes strategic divisionalization of oligopo1y with product diffa-

entiation and the implication of kee entry eqailibrium. This analyais can be viewed as a

geperalization of the modd of Corchon, Po- and Baye et al., sinœ it contains th&

model as a special case. Followiog convention, the competition is modeled as a two-stage

geme. Oligopolists chootie the number of identical autonomoas riva divisions in the first

stage, and all divisil ins engage in a Cournot cornpetition in the second.

Like Corchon (1991), Pol& (1992) and Baye et ai (1996), I show th& oligopolists

have incentives to 4et up d a t e r a & autonomous rival divisions, despite the fact that

profits are Iowa for each of them in equüibrium relative to the no-divisiondization case.

The eqaüibrium nuii~bet of divisions of eoch firm increases with the mbstitntability of the

differentiated prodii ct s and nith the number of cornpethg f h .

Divisiondizatio~i also ha9 sigdicant implication on entry. An entry can considerably

i n t e n e divisionalir ation and, consequently, the competition. The credible threat of

divisionalization in 1 he case of an entry makes divisionalization a n a t d entry deterrent.

As a result, an innimbent can enjoy an extremely high profit relative to the entry cost

withoat worrying a lioat an entry, when new products are to diffaentiate from

the existing ones. If an entry does occur, to soften competition, the entrant h a much

higher incentives to differentiate itself fiom the incambent relative to the case where no

divisionahation is dlowed,

The third essay investigates strate& leasing of production righte in U.S. onshore oil

fields. Oil production is modeled as a two-stage game. Fust, landownets choose leasing

strategies, and then, ail lease holders choose extraction strategies.

It is shown that landowners have incentives to subdivide unilaterdly their landholdings

and gant production right s to multiple independent operators, despite the fad that more

dispersed production concentration leads to a more serions rent dissipation in a common

pool oil field. Multiple leasing is a cornmitment mechasim for landowners to gain the

S tadrlebergleader-advantage in the production stage.

This analysis provides an explanation to a long-standing pnzzling phenornenon, i.e.,

the persistace of the widespreaà inefficient production organization in U.S. onshote oil

fields. Moreover, it has signifiant implications on general common property problems. In

the e x i s t a literatnte, the property onmer is txeated the same as the property operator.

This article, howem, shows that theg are nmally vety difterent and that the operation

stractare c m be much more dispased than the ownetship structure, becaase owners

have incentives to g~nt operation rights to multiple hdepepde~t agents. T h d r e , Winguishing the ownership structure from the operation structure and modeling the

relationship between them are essentiai to common property problems with ptivately

controlled acœss (not h e acœss) .

The anal+ in thtp dissertation is also closely related to, but distinct from the metger

literature ench as Salant et al. (1983) and Gaudet and Salant (1991), which e x d e the

impact of mergers on firms3 profits and on social welfare. Under plaueiile conditions,

they show that m q e r of a mbset of firms may redt in profit bris for the merghg

h, e v e . thougli merga le& to a more concentratecl oligopoIy. This disdation

de& with the oppsite iesue: the incentive kcing firms to divisionalize or to set ap

rival independent iinits. We show th&, under several different and plausible scenaiioa,

each firm has aailiiterd incentives to mate rival competing anits. Unlike most of the

merger literatare, NU analysis permit8 one to malyze the equilibritun conseqnences of

these incentives in a noncooperative setting that allows all firrmi to divisionalize freely.

The merger literat iire, in contrast, impliatly views merger as a eooperative game among

merging parties, f o r the set of firms that mage is nmdy exogenously selected.

Chapter 2

Complements, Subst it utes and

Strategic Divestiture

2.1 Introduction

Since the e d y eighties, corporate divwtitums have been a major fonn of corporate re-

strnctnring in the United States, accounting h r 40 - 50% of merger and acqoisition

activities. Divestitares (or sell-05) involve the transfes of a part of a firm7s business to a

new OW~WI, as opposed to the sale of the entire firm. The value of such d-offs reached

over $177 billion in the United States in 199617 and similar markets exkt in the other

industrialized economies. Both the volume and the nature of t h e transactions raise

questions bor the economics of orgaahation and h r corporate strategy. What determines

whether the cornplex bnadh of business activities that comprises a cotporation should be

either a freestanding, independent enterprise or, inetead, a anit of a large h? What

determines whethet a particular business unit should be divested, and if so, how?

In this paper, we examine a possible answer to these questions. More specifically, n e

focus on firms' strategic incentives of divestitirres that relp on product-line complemen-

tarities and prodnct market competition. We consider a simple environment in which

thae ate two b. Each fkm supplies a groop of complements, and the two groupe

of complements are i m p d c t substitutes. With this tuaenork, we trg to approximote

competition among eonglornerates, which are the main soiiras of divestitures. For ex-

ample, two cornpethg airline dliances, eadi of which consista of several regional airline

companies, have a conœptually similat structure. Anothez example is two cornpethg

shopping centers, each consisthg of a number of stores. The existenoe of transpodation

costs makes stores within a mail, even when snpplying substitutes in the normal amse,

transactional complements ex ante (A-, 1985; Stahl, 1987; and Beggs, 1994). We ad-

dress only the issue of strategic divestittues in such an environment, while the issue of

mergers can be aaalyzed aaalogously in a setting where each complernent is supplied by

an independent fh. We mode1 the firms' choies of divesting and pricing as a two-stage

game. The duopolists simultaneously choose th& divestiture strategies in the fist stage

of the game, and the independent divisions (the parent firms and the divested divisions)

compete in prices in the second. In order to highlight pncely strategic motives in onr

aaalysia, ne strip away 0th- factors that might dec t the tirms' decisions to divest, such

as moral hazard problems and inaeasing return to scales. In partidai, ne assume that

the technology of each firm exhibitr constant retums to scale and sape.

In this tamework n e first show that, when facing competition, fimu producing a set

of complementary products or services may h d divesting some of their complementory

products a profitable strategy. By divesting, a finn crediily commits not to mordinate

the priciag of complemeat s and, therefbre, softenlr competition to it s rival firm. On one

hand, this strategy makes the divesting firm more vnlnerable to its rival fum's potential

aggressive pricing. On the 0th- hand, softened competition wi l l increase the total psofit

in the market. If the gain in total profits outweighs the loss due to the vulnerability fiom

divestiture, then divestitnre is a profitable stiategy br a firm. Once its rival has divested,

a hm is more Lilrely to f d o w the mit since the vakierability tesnlkd h m divesting is

reduced. In the symmetric eqnilibrium, both f b divest and neither d e r s any loss in

terms of relative strength in competition. Both firms then gain hom the inaease in total

profits.

The results rely criticdy on produbliae complementarity and competition between

finns. In the absence of dmestitates, tao cornpethg firms set prim lower thm the

monopoly prices, which m-e the aggregate ptofits, for each firm ignores the positive

externality of its priang on the riva film's profit. After a h diveet= into independent

divisions producing complementuy products, those divisions ignore the negative exter-

nalities of theV pricing on each other's profits. When the degr= of divestiture is small,

the own-coup negative demeniy, which denotes the extemaiity of pricing among dm-

sions of the same firm, is smder than the mss-group positive extenidity, which is the

externality of pricing between h. Therefore, a s m 4 degree of divestiture by one firm

moves the prices doser to the monopoly prices, leadiag to higher profits. This reamning

works for both firmii. Indeed, when we chéuactde the mbgame perfed equilibrium of

the tw+dage game, we h d that both f h have incentives to dive& when competiag.

The degree of divestiture in equilibrinm is determined by both the degree of substitution

(or the severity of competition) aad the degree of eomplernentarity of each firm's product-

line. The more severe the competition among firms, the higha the incentives to divest.

Thus, chasging the competition environment soch as deregulation, trade liberalization

and entry may trigger divestitures. By divesting, mmpeting f i create own-group prie

ing extetnality to mitigate the opposite cross-gronp exteniality, resulting in higher prices

and profits.

OUI analysis hm important implications br the social welfPre consequenees of di-

vestitures. Conventional wisdom holds that mergers of h s mpplying simila products

reduce competition, increase the prices of the products, and decrease consamers' w e h e

and total su~plus. Consequently, mergers have been the main concem of regdatory au-

thorities. When divestitures are motivated by product-line complementdties, however,

we find that divestitares inuease prices, lower quantities, and decreaae consumers' welfase

and social surplus. Therehre, from a social welfate point of view , divestitures involving

complementary goods or services should be diacotuaged as mach as mergers involving

s~bstitates.~ The fict that firms can achieve tacit collusion in pricing through divestiture

when cornpethg product-lines mnsist of complements makes regulation a more cornplex

and difficult issue,

We also consider the situation in which firms are able to coordinate th& divestittue

dechions in the fist stage. It is shown that there e t s a pair of divestitare strategies

mch that the joint monopoly prices and profits are achieved in a non-cooperative p r i e

competition game in the second stage. In mch cases, by choosiiig the appropriate degree

of divestittare, cornpethg firme mate an orn-ppup negative extemaüty which exactly

2 0 i u tesuits in this context have a dose parailel with th- of Spnre (1976) aud Economidea and S.L0p(l992), who u y e that for c o m p l ~ f a r y pmducti, mctgem teduce p & a and incrame COMUOCI.'

welfsre.

offiets the cross-gronp extemality. Soch a mrdinated numbet of divisions is greata

than the number of divisions in the non-mperative game. This is due to a positive

externality between the firms' choiœs of divisions. Met divesting, a firm commit8 not

to wordinate the priang of its divisions. This fat-cat strategy softens the second stage

competition, raises prias, and thus benefits the rival fitm. Coordination between the

two firms internaüzes the positive externality and thus results in more divisions than the

non-cooperative eqailibrium permits. With non-coordinated divestiture, the ptices move

up but remain below the monopoly phces. With coordinated divestiture, the eqnilibtiam

p r i a are exactly the same as monopoly prices, as if a l l divisions of both firms are operated

by a single agent. Throagh divestitures, firms may achieve perteet collusion in priQiig in

a non-coopetative price game, which ia a striEing remit.

A variety of other arguments have recently been put brward to explain divestitures.

For instance, divesting is rationaiized by some as an institutional innovation arising in

response to the loss due to moral hazard problems in large corporations (Williamson, 1975;

Aton, 1988; Hart aad Moore, 1990; Holmstrom and Milgrom, 1991; Meyer, Milgrom and

Roberts, 1992; etc.). These theories based on asymmetric infozmation are certaidy asefal

in explaining the decentralization of the cuntrol of assets or business activities. They

have little power, however, in explainhg that many divestitures are of unite that had

been previously acqulled rather than started kom scratch by divesting firms (Porta,

1987; Ravenscraft and Scherer, 1987; and Kaplan and Weisbach, 1990). Roth Porter

(1987) and Ravensaaft and Scherer (1987) interptet those sales as recognition of failtue,

which would acmunt for the prewmed perfonnaao~divestitare W e . The eviden~

acrsembled by Kaplan and Weisbach (1990), however, suggests that less thaa one-thitd

of acquisitions that were later divested codd be considered failmes ex post. Our theory

M e r s from those aiguments by relating diveditmes to competition environments aiid

the natare of product-lines. We predict that increased oompetition tende to in tenw

divestitnre activities.

Jensen's kee-cash-flow hypothesis (1986) mggests that managers who are imperfect

agents of stockholders will have a tendencg to invest even in unprofitable bwinesses. The kequent asset sales hllowing hostile takeovers caii be interpreted as undoing exce8sive

and unpdtable conglomeration. hcreased discipline on managers 6rom the strengthened

market for corporate control in the 1980s reduœd such investments and might abo have

led managers to divest th& previous bad investments to avoid hirving th& companies

becorne sabject to hostile takover. Jensen's hypothesis is consistent with the hding that

the accotmting perf;ormanœ of the divedial( hm improves d e r the divestittue aad that

the apllotlp~ment effects are positive (John and OW, 1995).

The pnzaling side of this story is why the b d iavestmentri can be sold for more then

they are wodh to the curent orner. One of the prominent explasations admced is

that àivestitures are motivated by a desire to increase the bcas of a firm's business and

establish core cornpetencies. The underlying hypothesis is that perhaps more fomsed

firms pte easier to manage and so create greater values or that différent managers are

s m d in managing different types of assets. Sueh an explanation is not very satisfactory,

howevet, since it is hard to refute. In this papa, we provide an alternative exphnation for

a dass of diveditares where produdline complementarities exist between the divesting

units. Casual empmciam saggests that such complementarities ofkm &t3 Divestitiues

iacrease the total value of a firm because of the chaaged cornpetition stmct\ue and the

firms' strategic behaviors.

Our analyeis is related to, but distinct kom, the literatnre on mergers involving frms

supplying complements. Sdop (1990) aad Economides and S a h p (1992) show that, in a

Coumot duopoly mode1 with complements, mergers of two f b snpplfig complements

redace prices, because a merger d l o n s coalition fums to abriorb a positive extenielity.'

=For example, on September 20, 1995, ATYr announcd th& it would split into three indepen-

dent firms, with the f h t oflering longdiatance telephone and credit card euvices, the second supplying telec011l11lUIYcation equipmnt, and the third d&g with computer bushsee . These th- busiaesses

can be viewed as complementary. For details, see YATdtT's three-way split," The EmnomUt, September 23rd, 1995. Many 0 t h tclecom-equipment companies such aa Sweda's Ericsson, F i d ' e N o k , and the U.S.b 3Com entered the cornputer mauket aot long ago, but have now lefi the computer business.

Another example is shopping mails. We often observe that in-tom shopping mails con& of many

independantly maalaged shop which unully seil ordiuary complemenb. Différent iihopphg mails compek

by sehg goods which are aubetitutes saaa ni.Us. Eùrthetl~y)~:e, evwi if di&rent stores in a mal1 o&u

similar products, consumers are not soie which product they wodd prek prier to vieiting stores. Their d d o m arc often based on upected prices. TheseSom, the existence of shopping coets maLes ordirmy

subrtitutes within a mdl tramimtion complements (sc. A m , 1985; Stihl , U87; and Beggi, 1994).

P u h i g h and Gould (1995) provide emptiul evidence that p i t i v e Bgglomerate e x k n d t i e s ePlt when stores are Iocated togethn in a mall. Otu d y d s q l a i n r r why shope in shopping mills u e not omed

by a single firm. 4The tesults are also similnr to thaie in the vertical integratian litetafute auch as GmahPt and Ohta

Our concem is with the opposite issue: competing firms7 incentives to divest aad the

consequences. Ehrther, unlike most of the merger literature, which asuaüy modele mergezs

in a cooperative game setting, oar analyais of 6r.m' choies of organization hniui and

pn&g is conducteci in a non-cooperative game settiog.

This paper is also dosely related to the recent strategic divisionalization litaatnre,

such as Corchon (1991), Corchon and GonzdeeMaestre (1993), Po- (1992) and Baye,

Crocka, and Ju (1996). These anthors andyze the strategic incentives for firms to form

independent divisions when competing in a homogeneoos produd mstket. They find thet

firms tonn multiple divisions in order to take a liuger share of the market. Moremer,

divisionalbation leads to lower prias, lower profits and higher social weltare. This papa

aaalyzes a diflernt cornpetitive environment and identifies a Merent incentive far finns

to break up. In oar Lamework, finnrr with a set of oomplementary products set up

independent divisions to soften the cornpetition from th& rivals. As a r e d t , diveditue

of this kind inueases pices and profits, and reduces the social welfare.

For simplicity, the main part of our analysis is conductad in a setting where there are

two fmns, each supplying a group of p d c t complementary products or services. However,

the intuition and qualitative r e d t s carry over to more cornplex settings in which there

ate more thaa t a o competing firms, and produblines are imp&ct complements.

The rest of the papa is organized as bllows. The next section introduœs a two-stage

duopoly model with differentiated products. Each firm supplies a grmp of p&d comple-

ments, and aaoss finne, the products are imperiect substitutes. Section 3 characterizes

the equilibrium outcornes and provides the main results. Section 4 discasses possible

extensions of the basic model. Section 5 concludes the paper.

2.2 The Mode1

Suppose that consamers demand a number of dinizentiated producte, which are divided

into two gtonps. Within each group the ptodods are @ct complements and, across

groupe, they are imperfect substitutes. Let Nk denote the set of products in goup k,

k = 1,2. The demand functions ate @en by

for k, Z = 1,2 and 1 # k, where ph. and qk denote the price and qnantity of prodoct i in

g~oup h, respectively, and = znkl is the aggregate prie of produds in groop k, aad nt is the number of produds in group k.

Notice that the demand system (2.1) is symmetric both withia aad between gronpsP

We make the bllowing assumptions regatding the funetion D ( n , pl) Let P = {@i , R) E

R:ID(m,m) > 0, D(p2,rn) > 0).

where Dk(m, a) denotes the first-order derivative of D(pi, n) with respect to R, k = 1,2.

The ~esamption that Da > O represents demand substitatability between the two groups

of the products. Di + 4 < O dates that the effect of the aggregate pr ie nithin the grottp

on the demand (own-group effect) dominates the effect of the aggregate p r i e fiom the

other group (cross-group effect). To illustrate our analysis, ne hequently use the liaeax

tom of demand functions

where u > 0, /3 > 7 > O. The ratio, y/& mea8nres the degree of substitution between

the two groups of products or the extent to which the own-group effect dominates the

ctoss-g~oup effect.' When = O, the two groups' products are independent; when

7//3 = 1, the t a o goups are p d c t substitutes.

There are two fiime, 1 and 2. Firm 1 supplies aU the gcmds in the first group and

firm 2 offets dl the complements in the second! To focas on the strategic incentives, we

=The eymmetry of demanda aaaur groupa is not aucial fm our diseuasions below. assumptions are standard in the literature on difhmtiskd pmducta. Ses E b b a n (1977)

and Deneckere and Davidson (1 985). ?Be(Ig (1994) uses the samc linear dnnand hction. There art only two complancntr within euch

goup in his model. dtetnative speciûcation of the modd is to aamune that the total nPmba of fimm ia nt + na .ad

each firm supplies one prodtlct. The ime of strategic incenthm to m e can k addrCInICd in t b aetup.

assume that the production technoIogy of each firm exhibits constant retums to SC& and

smpe? That is, the total cost fanction for firm k is

where is the constant marginal cost of produchg product i in group k, aad % 2 0.

We consida the mbgarne perfèct equilibria of the hlloniag two-stage game with per-

fect information. In the hst stage, the two îùms simultaneously choose theu testrocturing

strategies. In stage two, a l l independent firms compete by simdtaneody setting pries.

By restrnctnring, the parent fkm keeps a subset of its product lines and sells the net

of its operations to independent entrepreneurs (not to its rival firm). It shodd be noted

that, in otu fiamework, the restructming strategies of the finns can be any of divestitare,

spin-off, breakup, or divisionalization, as long as the redting f h independently chmse

th& pricing strategies. In the following analy sis, ne simply tefer to a restrnctariiig choie

as divisionalization, namely, a f i setting up autonomous rival divisions.

We mode1 divisionalization of a hm as a partition of it s produd space. Let dk denote

a partition of 4, and each c d in the partition be a division of firm K. Let mi: be the

nnmbet of divisions in dk. Given a pair of strategies (dl, d2), the profit fundion of division

j in poup k is

where, h r notationd simplicity, n, and Qi represent the aggregate price and the aggregate

mazginal cost of the products in division j of gronp k, respectively, and A = xy,L, Bj is

the aggregate price of products in group k. For k = 1,2, let

whem 1 # k, and 4 = zd1 ckj is the awegrte matpinai cost of the produds in gotap k.

A divisionalbation (or divestitnte) strategy caa be viewed as a set of taire-it-or-Lave-it

contracts signed between ftm k (ot the parent km) and independent entrepieneus. Each

9The ammption of constant rehunr to scop implies th& thae is no operathg synergy between dif-

fisent b e a of buin-. Oiu modd is motivahi to adcirem divestiture h e a concerning con&lo~~~~rates.

contract spe&es a terne pnce at which the parent firm is willing to sell the operationcl

of a subset of its products. We assume that the contracts are restrictive so that no division

c m farther divide or snbcontract pMs to the price decisions in the second stage of the

game.1° It is then reaaonable to assame that fùm k sets a reserve pr ie equd to the

profit that division j can malte in the second stage game, and that each entrepreneur is

indifferent about acœpting the conttact or tejeding it . Therebre, the total profit of firm

k is given by (2.4).

The two-stage game can be solved via backwaxd induction. In the second stage of the

game, for any pair of strategies (dl, d2), each division j in gronp k chooses its ptice B,

to manmize (2.3), given the prie choies of other divisions within and across groops. In

the hst stage, firm k chooses a diviaionalization strategy, dt , to m-e (U), talMg

into acconnt the divisionaüzation choie of the other finn and the eqdibritam prices of

the second stage game.

To simpiify our presentation and emphasize the effects of the nature of demands on

divisionalbation, we set all the marginal wsts equd to zero. This simplüication does not

dec t the qualitative r e d t s in the paper.

2.3 Analysis

In this section, ne first htrodnce two benchmarks. One deals 6 t h competition between

two firmil without divestitare. The other is the joint profit m-ation. We then

characterize the eqdibriinm outcornes of the two-stage games, which can be solved by

backward induction. For each set of divisions chosen by the two firms, the eqnilibriurn

of the second stage pnce game is determined, and comparative static properties of the

eqailibrium are discussed. Our main hdings are then p-ted.

2.3.1 Two Benchmarks

In the first benchmark, two finas dkctly engage in Bertrand price competition without

divestitute. That is, dl and da are singletons and equd to Ni and N2, respeetively. Given

the simplification of the muginai msts, fhm k haa the following profit faaction:

1% the divisiom un huther dinde beke they choose priccs, the p m b h becornes very compiicated.

W e are ciurently wotking on this hue.

for k, 1 = 1,2,1# k, aad = xi., m. Notice that the profit fundions depend only on

the aggregate p r i a of the complements, R and R. Each firm only needs to decide on ita

aggregate price, and individual prices am indeterminate. Ehrthamore, the profit fundion

of firm k inueases with the price of the other b, since the prodacts acrosa groups are

substitutes. In otha words, there exists a poaitioc eztenrdity between the two prices.

In equilibrium, firm k chooseri n to r n u h n k (2.5), given the aggregafe pnœ of the

other g m p , R . The first-order conditions are

for k, Z = 1,2, and I # k. The eqnilibrium price (pl, pr ) is determined by (2.6). Let

be the elastiuty of demands in grmp k with respect to its onn price, B. Eqaations (2.6)

then hnply that, in eqailibrium, the tao fuma set th& prices such that th& demand

elasticities are eqaal to 1. Givem the symmetry of demands aaoss groops, in equilibriom

pl = f i , which we denote by p. Later, we niu provide sufEcient anditions for the

existence and uniqneness of the e q u i l i b h for this game.

In the case of linear demaad h d i o n (2.2), the best-reply fundions fiom (2.6) are

easily computed as

which are linear and stridly i n c r k g . T h d r e , two prices are drotcgic complements,

in the sense of Bulow, Geanaltoplos, and Klemperer (1985). The eqtiilibninm p r i ~ is

and the eqabrium profit hr each îum is

In the second benchmark, the two firmr, do not divide bat collude by setting pnce8 to

manmiae their joint profits:

Clearly, in thh optimization problem only the aggregate prices matter. Assume for now

that the global maximum is unique. Given the symmetry of II(pi, pr), the optimal ag-

gregate prices are identical and denoted by PM, which is determined by the first-order

condition

Let I ) L I ( P ~ , R) P pkD2@t, n)/D(PL, R) be the cross elasticity of demands between the two

groups of products. Then (2.8) can be rewritten as

Thesefixe, at the monopoly solution, the own price elasticity is set to be 1 plus the cross

elasticity. Since the aoss elastiaty is positive, the own price elasticity at the monopoly

solution is greater than 1.

Compated to the hst benchmark, the pint profit m-ation intemaJizes the ex-

ternality between the p r i a of the two gronps. As a r e d t , the monopoly ptice, p ~ , is

greater than the non-cwperative eqnikiirium prîce, 8. This point can be k l y f i s -

trated fbr the linear demand fnnction (2.2). In this case, II(pl, m) is strictly concave. The

monopoly price and joint profits are computed as

The monopoly price is greater than the duopoly pria, and monopoly profits are higher.

2.3.2 Second- Stage Price Game

We next analyze the equilibrium outcorne of the seand-stage pria game. For a given

paix of divisionalkation sttategies (dl, dg) , the profit fiindion (2.3) of diviaion j in gmup

k can be written as

far k, l = 1,2, and 1 + k. Division j chooms its prioe, nj, to manmize (2.9), given

the price choies of the other divisions both within and across groups. The kstordex

condition for an interior solution is

for k, 1 = 1,2, and 1 + k. Pue-strategy Nash equilibria are then determined by equations

(2.10). Li eqdibrium, each division sets its own elasticity of demand, ek j(m, A, R ), equd

to 1, where

Notice that, by (2.10), the equilibrium prioes of the divisions within the poup axe

identical. Thtas, the equilibrium conditions (2.10) axe eqnivalent to

foi k, 1 = 1,2, and I # k. Equations (2.11) determine the best-reply firndion 6or group

k and, hence, the equilibriam aggzegate prices. T h e are interesthg ptoperties of the

equilibrium. The h s t is that the own pice elaeticity of gzoup k equals the niunber of

divisions in that group, i.e., R ) = mc. This implies that each firm can inmase

its own price elasticity by setting up autonomous riva divisions. The second property is

that only the number of divisions mottas, not the nomber of products in each division.

Thus, a pair of dmsionalization strategies (di, d2) can be s t l ~ ~ m d by a pair of division

numbers (ml, ml), wheze rnk 5 ni: bt k = 1 and 2.

Fùrther aseumptions on the demaad fundion axe stated to guarantee the existence

and uniquenese of equilibrium in the p r b s e t t b g game (see Ehiedmaa 1977, p.72).

Eere Du(a, R) denotes the second-order dezhative of D(pii, R ) with respect to fi and

R , k, 2 = 1,2. (A2) states that the demand fandion is concave with respect to the

own-group price. This condition is d c i e n t for the concavity of rk, with respect to

fi,, which is the second-order condition for a maximum. (A3) states that the Maence

between o ~ - ~ o u p effect and cross-groap d e c t klls as the own-groap price goes np. (A2)

gu~rantees the existence, and (A3) the nniqueness of eqdbrinm. (A4) implies that the

bestreply functions determined by (2.11) ate strictly increaeiag. Thus, the p r i a between

the two groups are strategic complements. This is a common assumption in the fiteratare

on price cornpetit ion with diftérentiated product S. Some inkresting comparative-st atic

results can be obt ained in this case. Let f i and f i denote the eqnik'brium aggregate gronp

prices, respectively, and ik = D(&,fi) , for k, 1 = 1,2, and 1 # k denote the eqailbrium

qaantities.

Notice that the above assnmptions me satisfied h r the lineax demand function (2.2).

In this case, the best reply functions determined by (2.11) are

which are lineaz and strictly

inaeases, the best-reply line

inue!asing. Figure 2.1 ülastrates the best-reply lines. As m k

br gronp k shifts up, but the best-reply line br gxoup 1 does

not change. Thefixe, eqdibrinm pnces fat both groups inczease 6 t h m&. These p r i a

can be easily compnted as

For the genezal tonn of demand fanctions, ne have the hbwing characterization and

19

comparative statics.

Lemma 2.1: Suppose that (Al)-(A3) hold. Then, for each pair of (ml, ma), there exkits

a unique eqailibrinm in the price-cietting game. hrthermore,

(a) the eqnilibrinm prices are identical within a groap;

(b) the aggregate price in group L, a, inme- with r n ~ for k = 1,2;

(c) the aggregate price in gronp 2, R , inmeases 6 t h mr; for k, 1 = L,2 and 1 f k, if

(A4) holds;

(d) the equilibtinm quantity of each complement in groap k, ek, decreases with mk

for k = 1,2; and

(e) if ml = ml = rn, then pl = a increases with rn, and = g decreases with m.

The proof of Lemma 2.1 is given in Appendix 2.A. The intuition for the monotonicity

of the aggregate group price with respect to the number of divisions in the g~oup is the

followhg. Since the products within the gmup are complementary, there ie a negatiue

ezterndity among the prices of these products. In other words, an inczease in the p r i a of

one product rednces the demand for the other products w i t h the same gronp and, hence,

decreases the profits of those produds. If the f i is divided into independent divisions,

divisions d l not take t h extmality into acoount. In eqnilibritl~~l, the aggregate prices

of the complements within the group increase when more divisions compete against each

otheI.

Fhn (2.11), an inmease in mk shifts np the best-reply m e of grmp k, but does

not change the best-reply m e of group 1. Given (A4), the best-reply cuves for the two

g~oups are upwud-sloping. Thezefore, both prices inctease as mk goes up (clee Figuxe

2.1).

Lemma 2.l(d) states that the eqnil'brium quantity of each complement decreases with

the number of divisions in that group. As the number: of divisions in the 0th- gzoup

gœs up, however, the eqailbrium qnantity of the complement d e s not neceasarily fall.

It depends on the sizes of both mi and ms. What ne know is that when the fums divide

gymmetricdy, i-e., mi = mz = m, the e q n i l i b h qnantity of each amplement decreaaes

as m inueases.

2.3.3 Strategic Incentives to Divest

We now examine whether a divestitiue improves the h' profits. Given the characteri-

zation of the eqnilibnnm in the seand-stage pnce game, ne cam write the reduced-8otm

profit fnnction of firm k as

for k, 1 = 1,2 and 1 # k, which depends only on the numbers of divisions rnc and mi.

In the rest of this section, ne treat ml and mg as continuous variables. In Appendix

2.B, n e illustrate that the qualitative results in this paper still hold when ml and ma axe

restricted to be integers. The profit of firm 1 depends on ml through the two prices. The

derivative of firm 1's profit fanetion with respect to ml can be compated as folows:

U&g the fitst-order conditions (2.11), ne can write the own-gtoup effect of the pBce on

the profit as

which is negative for ml > 1. Therehre, by Lemma 2.l(b) and (c), aa increaae in ml hair

two effects on fiim 1's profit. The kst is the own-group dect : it increases the aggregate

prie of products in group 1, which reduces firm 1's profit due to the negative extemality

of prices withia the groap. The second is the aosagroup effect : it inaeases the aggregate

pria of produda in group 2, which ipcreases fmn 1's profit due to the positive externality

of prices across gronps. When mi is close to 1, the own-pup effect is close to zuo, and

the aoss-gmup effect is positive. This meaas that a small degree of divestiture by îum 1

increases its total profit. If the deg~ee of substitution between the tao groups of prodacts

is high, then each fkm has an incentipe to &vide nnilaterally into maltiple divisions.

Next, ne determine the non-cooperative eqdibrium of the Grst-stage division game,

where the firms independently chooae th& numbets of dmsions. Each h chooriea ite

namba of divisions to maximize its profit, taking the 0 t h firm's n u m k of divisions

and the second stage priang behavior as given. Ushg (2.12) and (2.131, we can rrrite the

kst-order conditions for an interior solution as Wows:

for k, l = 1,2, and 1 # k. The non-coopexative eqtiik'brium is determined by (2.14).

Since the redaced-brm profit fundions are symmetnc in ml and ml, which we denote by

symmetric eqnilibtium. We denote by T% the symmetric eqailibrium namber of divisiona.

To determine the size of the eqailibrium number of divisions, T%, we impose a furthet

restriction on the demand fnnction:

Simüu to (A3), (As) dates that the difference betwan the own-goap effect and the

cross-group effect does not increase as the cross-groap pria goes up. Both asstunptions

impose a limit on how the net effect vaxies with prices. (A3) and (A5) together imply that

the degree of substitution at the symmetric price, -a@, p)/ Dl ( p , p) , is non-increasing

in pnce p. In the case of the linear demand fundion, (A5) is obviously satidied. The following lemma illustrates the important properties of the reduced-hm profit fnnction

when the finns divest eymmetricdly.

Lemma 2.2: Suppose that (Al)-(A3) and (A5) hold. Then the reduced-dotm profit func-

tion V(m, rn) is a singbpeaked function of m and reaches the maximum at m = mm,

where

The proof of Lemma 2.2 is presented in Appendix 2.A. Lemma 2.2 implies that a s m d

degree of divestitures by both firms increses their profits, but too many divestitttres can

reduce their profits, provided that mm is leai than ni and n2. We non state otu main

r d t .

Proposition 2.1: Suppose that (Al)-(A5) hold. Then the symmetric eqnilibRiua num-

ber of divisions, 6, satides the inequalities 1 < r% < m*.

The proof of Proposition 2.1 is presented in Appendir 2.A. The aaipueness of the

eqnilibrium in the division g-e req* fnrther restrictions on the demand fnndion.

We do not provide the exact restrictions here. Instead, we use the lineat demand fundion

(2.2) to illustrate Lemma 2.2 and Proposition 2.1. ki this case, the eqaübrinm payoff

from the price game can be compnted as

It can be e d y v d e d th& V(mi,ma) increaaes stnctly with ma. Thas, there d s s

positive externality between the finns' choices of divisions. The beet-reply fnndions in

the division game are ml = R(m2) and ml = R(ml), where

which is strictly increasing and always p a t e r than 1. Figure 2.2 illustrates the best-repb

m e s that cross at the point (h, h), where

It can be verified that V(ml, m2) is a single-pealred fanction of ml, which parantees

(fi, 6a) to be a Nash equilibrium of the division game. Fnrthennore, the eqailbrinm is

unique. It foilows hom Lemma 2.1 that the subgame p d d eqnilibrinm of the two-stage

game is unique and symmetric.

To illustrate Lemma 2.1 and Proposition 2.1, we can e d y ve@ that V(m, m) is

single-peaked and teaches the maximum at

Cleady, fh is greatet thaa 1, but less than nt*. Fat any î b d /3, both rh and mm hue~se

with 7, which meamires the degree of substitution between the poups of pmdnds. As 7

goes up, the competition between the two groupa intensifies. Cornpethg firms respond

by divesting into more and fina independent division8.

We non discuss the welfaie implications of the eqnilibrium divestituxes. Suppose that

the demand system (2.1) is derived fiom an aggregate ntiüty ma,ximization snbject to s

budget constraint, where the aggregate utility fimction takes the following h m :

where the good po is a numeraire, and U(*) is a monotone inereaeing fanction. It hUows

that the consamers' surplus is

and the social surplus is the consumer's surplus plus the finns' total profits, which is

simply SC = U(qll, ..., ql,,, qal, ..., q2,& App1ying Lemmas 1 and 2 and Proposition 1,

we obtain the following w e l f w implications of the eqnüibrium divestitures:

Corollary 2.1: Suppose that (Al)-(A5) hold. Then the equîlibrium divestitures inaease

the fitms' profits and reduce the <r>nsnmers' welfare and social stuplus.

The implications for the socid welfare ansequences of divestitures are notewodhy.

Conventiond wisdom tells us that mergers of finas sapplying homogeneons products or

imperfect substitutes (with qaantity competition) reduce competition, increase the prices

of the products, and decrease consumers' w e b e and social SO~P~US. In otu model, di-

vestitures axe motivated by product-he complementuities. CoroUaxy 2.1 and Lemma

2.1 imply that snch dmestittues increase priœs, Iower quantities, and deccease consumerd

welfare and soud slltpIus. Thetefore, h m a social w e h e point of v i a , divestitntes

involving complementary goods or S a n a s shodd be disconraged as much as mergers in-

volving substitutes. Iii practice, however, regdatory authodties are osually con- only

about mergers, but asudly not about divestitntes. The possibility that cornpethg firms

can achieve tacit collusion in pricing tbough divestitures, rather than thmugh mergers,

rnakes antitrust a more cornplex and difficult issue.

2.3.4 Coordinated divestit ures

In this snbsection, ne consida the situation ui which the fitms ate able to mordhate

their divestitare decisions in the first stage. We show that there exista a pair of division

numbezs (ml, ml) such that the joint profit maJcimizing prim (pM, pM) ciin be supported

as a non-mperative equilibrinm outeorne of the pna+setting game. This pair of division

numbets turns out to be (m*, m*), defined in (2.15).

Lideed, aimpating the eqailibrium conditions (2.11) for the p r i e game with the neces-

sary condition (2.8) br the joint profit maximization problem, ne find that the joint profit

maximizing prices satisfy the Nash equilibriam conditions, if mi = ma = m8. Notice th&

m* = U(N, pM), Le., the number of divisions is equal to the own price elasticity of each

group at monopoly prices (or 1 plus the a088 elasticity). A positive degret? of substitu-

tion between the two gtoups of prodacts implies that m* > 1. Since Lemrna 2.1 provides

s&cient conditions for the existence and miqoeness of the equilibrium, it hllows that

the joint profit maJcimizing prices can be supported as a unique e q P ü i b h outcorne of

the pria game if both ftms break up into rn' number of independent divisions. In othet

words, when the firms are able to motdinate thek choies of divisions, they can replicate

the monopoly profit. This provides an alternative way h r the 6 . m ~ to collude.

Propodtion 2.2: Suppose that (Al)-(A3) hold and Min(nl, n2) 2 m*. Then, by set-

ting mi = rnz = m*, the second-stage price cornpetition yields the pint profit

maicimiPng prices and profits.

The iogic bebind Proposition 2.2 eaa be described as bllows. Since the joint profit

fundion (2.7) can be remritten as the sammation of the profit functions (2.9) over all

independent divisions kom both groaps, the pint profit maiamization problem can be

eqaivaiently solved by choosing prices (hi, ..., pl,, ) and hi, ..., n,). Notice that we

can decompose the effect of an inaeaae in pice m j into the following t h e tenns:

The hst term in the sqoare brackets represents the own-group effect of the price on the

profit of division j in group 1, ni,, which is the same as the ledthand side of (2.10).

The second tenn is the aggregate intra-group effect of price on the profits of the 0th-

divisions in the same gronp, rï, bot all j' Merent hom j. It is negative since divisions

within the same group supply complementary products. The third term is the aggregate

inter-group effect of pria on the profits of the divisions in the otha goup. Since productr

are imperfect substitutes across group~, the agregate inter-group effect is positive.

Now, if there exists a number of divisions m sach that the negative intra-pup effect

exactly offiets the positive inter-gmup effect, then the necessazy condition for joint profit

maxbhation is equivalent to the firat-orda condition (2.10). In other words, giuen the

number of divisions m, the necessary conditions for joint profit maximhation are identical

to the first-ordes conditions h r a non-cooperative equilibtnim in the price game. This

can be accomplished by sdting the second plus the third term on the left-hand side of

(2.18) equal to zero. Imposing symmetry aad substituting p~ tor pi and f i , ne obtain

The solution to (2.19) is ml = m'. A similat atgument d d d e s ml = mm. As a result,

the monopoly price p~ satides (2.8) and (2.11) and, hence, consists of the unique solution

to the joint profit maximization problem and of the eqailibrium of the pr ie game.

The driving force behind this finding is the cornmitment power of diveditare combined

with the extended product space, which indudes substitutes as well as complements. P r k

to divestitnre, the prices of products in each group axe set coordinately. After divestiture,

the firm credibly commits not to set prices of the group coordinately, therefbre induchg

less cornpetition fiom the rival group. As a r e d t t , the prices and profits increase. This

implies that price coordination by a group of firms supplying complements d œ s not nec-

essady benefit the firms and harm consumers. In OUI model, the la& of coordination

among the prices of complements indeed leads to higher profits and Iower consumer sar-

p h . In other woxds, fimis have incentives to tie th& own hande in order to induce a

better (more profitable) response hom th& rivalsl?

The importance of incorporating both substitntability and mmpternentuity rithin

the same fiamework cm be seen dearly in terms of externalities of each division's pricjng

"A similar cornmitmilnt e&t works whea f- use a mt-fivoted-cusfomtr poky to raise the p&os

(as Cooper, 1986).

decision. There is a positive eztemdity between the pzicea aaoss groups due to eabsti-

tutability. Divestiture in the firststage mates a negatiue ezterndity of pries among

independent divisions within a groap. This negative externality caa ofEset the positive

externality. When the degree of divestitnre is srnail, the positive externality dominata.

Wheii the degree of divestiture is large, the negative exteniaiity outweighs the positive

one. At m = mm, dl externalities are neutralieed, and mnaequently, the monopoly out-

corne is achieved.

W e now undadand the second inequdty in Proposition 2.1. it is d r i v a by the

positive externality between the ftms' choies of divisions. Given (A5), an inaease in mi

will inaease finn 2's profit, when both firms choocie the same number of divisions. In the

preeence of such a positive exteniaiity, a lack of coordination between the f k n s r e d t s in

a smaller equilibrium number of divisions thaa the mrdinated number of M o n s .

What d e t d e s the size of the optimdy coordinated number of firms? Notice that

the ratio, -DZ(pM, pM)I& ( p M , p M ) represents the degree of substitution between the

two goaps of the products. The bllowing oorollary provides a comparative-static rewlt:

Coroiiary 2.2: The optimdy coordinated n d e r of divisions, m*, increases with the

degree of substitution between the two goups of products.

In one extreme case, where t hee axe no substitote goods, mo is eqyd to 1, and

each finn should monopolize the supply of the complements and ne= divide. In the

presence of cornpethg substitutes, the finns have incentives to divide. As the relative

degree of substitution between the two grotaps of complements incfeases, the positive

extetnality incteaaes and, hence, each fkn should split into m o n divisions to inaease the

negative extemality and mitigete the positive one. At the othet extxeme, if the number

of complements in each groap is small or the degme of substitution is large, fnrther

divestiture may not be possible. In this case, monopoly profit cannot be replicated, and

the finns p r e k complete divestitnte in which each product is suppüed by ui independent

firm.

2.4 Extensions

In the previous section, n e have discussed the déct of product market cornpetition (or

prodnct differentiation) on divisionalbation and shown that a &ha degree of substitution

between the two gronps of products leads to a pater number of divisions in both p n p s .

There are 0th- factors that determine the ccmrdinated aad non-cooperative divionaüz*

tion stsategies and the sapes of the fùms. They indude marginal costs, osymmetric

demmds, i m p d c t complements, and severd groups of complements. Ii this section, we

btiefly discuss only tao of these factors, imper&& complements and the number of gronps

of complement S. For simplicity, we use lin- demaad fanctions.

a) Irnpefict Complements

In our basic model, we have considered only perdect complements within the group.

Our andysis can be extended to the case of imperkt complements. To illustrate, we

consider an example with the hllowing linear demand functions:

f o r k , l = 1 , 2 , 1 # k , i = 1 , 2 ,..., n ~ , w h e r e a > ~ , ~ ' ~ ~ > ~ > O , a a d ~ = ~ ~ ~ ~ ~ . The assumption /3' 2 /3 implies that product i aad any other prodact within the gronp are

impertect complements and that the eff& of the price pm on the demand for product i

dominates the intra-group effect on the demasid h r any other produd within the group.

As before, /3 > 7 means that intra-group effects outweigh inter-gmup effects. The demsnd

system is symmetric both within the group and between p p s .

Notice that the demand fundion for prodnct i in the hst goup can be written as

which consists of two parts, the fist dependhg only on the individual price pli and the

second being the seme as the demand fnnction (2.2). Clearly, /3' - B does not &ct

the demand extemality arising h m aa inaease in ni* Remember that the optimally

mdinated number of divisions is determïned by balancing the negative and positive

extefpalities of the prices. T h d r e , it is independent of B' - and can be computed as

ma = /3/(/9 - 7). However, j3' - /3 anectr the Nash eqdibrium number of divieiom, fi.

It un be e d y deaLted that 6a ir deteriruned by the hIlowing fitstordet condition

whae ni and n2 are aacmmed to be eqyai, h r >tpliaty, and denoted by n. Notiœ th& th deereaaes with 8' - B. Whai the d e ~ n d elaaücity with respect to own price incmum

(&ha B'), the inmtives for eaeh fum to dmde f 9 becausa the second-dage e&bntlfn

prias decreaae. As a result, the eqdibrium number of divisions decreaes as /3' increaees.

b) Multiple Groups of Complernents

Our a d y é can elso be extended to the use of many p u p s of complemeite, whae

the produch are i m p d c t mbstitukr ocioss groope. Let K be the number of pupr,

K 2 2. The demand function oDr a complement in p u p k M lineru and presented by

Lr k = 1 ,...,Kandi = 1 ,..., nk, wherea > O , /3 > ( K - l ) r > O , nb is thenombaof

complenients in gonp k, and fi = =&, is the total prie of the complementr in goiip

k, k = 1, ..., K. The demand tDt other products is symmetrk with the groop and across

gr-ps*

We can cornpute the opthxdy coordinated namba of W n s for each g o o p aiid

the non-cooperative eqyili'brinm number of divisions as hbws:

As bebre, the optimaIly cuo~àinated nomba of divisions and the eqiiih'bhn nomber of

divisions inaease when the degee of substitution between the groupr of the pmducfs

incteaser. An interesting cumparati.static d t is that both mm and rî, in- rith

K. As the number of gronpr of the c o m p h t s goes up, c0mpeMion a c m s goiipr

in- and, hence, the magnitude of the positiPe externalities a,mong the ptiar acro8s

groupa also hueases. To mitigate the i n a u r d pomtive extemalities, the h n s n d to

mate more negative externalities by dividhg the h into mon independent divisions.

T h e d k , both the o p t W y coordniated number of divisions and the non-oooperative

eqailibriwn nnmber of divisions i n m .

In this papa, we have ugued t h d a h produchg a p u p of c o m p h t s can genetate

bigher profits tiuough direstitatee when there is a competing finn supplying an impabect

substitute p o p of complements. By delegating picing decisiuns to independent d i 6 sions, eoch fkm aedibly cornmitir not to set the pricea of the complements rithia the

groap coordiaately, which softens the cornpetition between the tm &ms. OPt anaijais

suggests that indudry strnct9n aad s k of fimu are dosely related to the natan of

heterogeicous producte and the strategic mnsida.tioni of the firme.

The welfue implications of the division~atioas in our models an eianificant. It is

shown th& fkms snpplying complairents have incentives to &est when facing competi-

tion, and the tesulting divestittues raise prias and teduce consumers' surplus. Honever,

the ptofit gains are not large enough to compensate the comamers' losses. As a result, the

total stuplus is reduced. This enggests that, h m a social welkre point of view, divedi-

t m a invol*&g complementaq gmda or services cm be as harmdal or magesa involvuig

substitutes. Thus, antitrast authoritws shoold be mnaerned about not only mergera, but

.180 diveditues. Yet, in practia, mergers are usaally the sole hcus of mtitrtlst policier.

Another implication of our anaiysis à that diveditares motivated by product-line

eornplerne&uities caa be viewed as a tesponse knrards èntry. Suppose th&, initidy,

thee îs a moaopoly that supplies a gmiip of complementaxy goodr oc &ces. Ckdy, in

otu aontext the monopolist does not have aqy inœntivea to divest itr operations. When

potential rivals enta the market, the monopolist hati two passible responses. One b to

compte ditectly against the entrants. If the entrants do not make enoogh ptodta to

covet theis entry a s t s , the &hies can then Le detened. If the produdr o k d by the

entrants ore ddkentiated enou& h m the hcombent'r producta, and if the entry mots

w relafively sumû, the entries m o t be detexrd In thb we, an optimal stzategy bot

the incumbent fiun is to &est Mgae of itr operatîonr to rab the cornpetition.

It ahodd be noted, finally, th& om andjais b baied upon a numbe~ of ~s8omptions.

One cmcial ~sumption ia that divisions a m o f Met divide behre they choose thm

pnœs. This is tsoscmable in situations, where the parent firmi di have major oroarhip

contiol of the divkbm, but do not make mmagement deddons. &o11rhiw? wnfradr

un be viewed as an eumple of such a divbionalîzation. In o t k situations, it un be

diffidt ter b u s or divisions to make thîs type of ammitment. Divieions may then have

incentives to divide fiuthet. Thiil taises the ism of what d e t h e s a &able i a d q Btrndaie in the presenœ of both substitutes and complements. M e r research abng

t h line ia needed. Our modehg of the dempnd structure a h Mpliee that piodudr

m a 8 groupe am not compatible. When they aze complet$. compatible, the demrnd

h d i o n has to be adapted. F i divesting dechions wi l l be aikcted. Therebre, our

analyyl doea not apply in the case of ctoss-gonp product mmpatibility.

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Chapter 3

Product Differentiation, Strategic

Divisionalizat ion and Persistence of

Monopoly

3.1 Introduction

It is generdy acœpted in emnomics th&, in markets aith Bimilsr producta, competi-

tion reduœs firme' profita. Yet, luge firme o h eet up independently managed rival

divisions1 supplying similPt producta and cornpethg in the same market2. A similat poz-

z h g phenornenon is that, to a cettain degrex, kanchiaee of the sune parent dirm are often

'For raunple, maay aufonu,bilc manuktuicnr have independcntly mamged operathg divisions. in

the ua of Generai Motoma, S b (1963) noka ' A c c o m to G e n d Motom p h of Orgsriirstion

... the activities of my rpcei%e operatiopi ut undet abedute ewtml of the hcetal I k h m g c ~ of that

Di*mon, mbject only to vety b m d contact rith the genetal o h of the Corpotationn@.1û6). Iiloodyi

umc car with difkmt namc platm, u are the C k p l ~ b r y r l a GqmzatioDk Piyzmtath Vqaga a d hdge

gmed to compete hz the s a m e customers. Them am a fan difbmt expiauatiom for

such practices. First, pducfion efaciency requires mnltiple prodaetion p h t e undet de

creasing retnrns to scale technobgy. b d , the need to sath& hetaogeoeous mn~llt~~ezs,

in tams of either tuta or location, htœs firmil to set up mdtiple divisions pducing

dl&?rent brmàs or mdtiple outlets operathg at dinaent locatbnrr. Third, it is uped

by Williammn (1975) th* sethg op autonomous divisions allepiates incentive pmblems

due to moral hea.td within large org.niaatiot18. Nevdheless, these explaaationr do not

juetig why a km allows iti, cibbbns to compete ratha thui to cooperate 6 t h each other

in prodadion (or SA) strate-.

To -ch bDr a more ratisfactory explmation, reant stuclier have fomsed on firmi'

sttafegic incentives in WonaJization. Schwartz and Thompeon (1986) snd Vixmdorp

(1991) show that the incnmbent firm can h&dl entzy by setting ap mdtiple r i d divigions prix to entrp. Cotcihon (1991) and Po- (1992) analp a two stage division-

rüaation game with a duopoly supplying homogeneuua produds. They show that each

km has an incentive to sd up rival divisions, but there is no hite Nash eqdibriiom.

Using a similair fiamewozk, Corchon and GonzbMaestre (1993) and Baye, Crocka and

Ju (1996) rectify the nonexistence problem by imposing either an exogenow bound of

p a m i s m i . l e number of divisions or a f k d M o n &-up ad.

The insight from these recent studïes is the QIlowing: in the homogeneous product

market, setting up a new independent division reduces the a%gteg&e profit due to the

increaaed campetition, but increures a h ' s shan in the aggregate output and profit.

The second dèct alwaya dominata the f it if produde of Misent fimu am @d

substitutes. Comequently, f h s have a prioate inœntive to divisianalize. Fûrthermore,

th- is no finite eqiiilbriirini because of the dominanœ of the second dect.

In t h paper, we provide a mode1 of Werentiated products, which contains the pre-

vioor framework mnaidered by Cotchon, Polaslry and Baye et. al. as a s p e a ws,

It is fint shown th& the problem of nonexistence of an interior subgame paaed Nash Eqaik'bnum (SPNE) in this likratpte is due to the uurunption of hornogepeous p d

uds. Product di&ereatiation abne anoam the existence of an interioz SPNE. AB h w n

in p d o u s studk, divisionaation has two e&cts on a fumtir profit; setting op au-

tonornous dittisions ~~~s a hm's market ahaxe, on one hand, and a a t e s mmpetition

h r the bu's d i n g divisions, on the other. W e d i s to the firrt eîFect aa the baninege

sterliry dec t , which by i t d enhances the firmyr prdtability, and the second as the

cornpetition egsct, which reduca the h ' s profitability. Pmduct diîkentiation w e k

the buSrnese stealing e f t ' becoase of the reduœd substitutability among produds. The

cornpetition de&, howeper, inauaes with p d u c t Meteptiation, &ce the competition

h m additionai divisions iii borne mon by exidhg dioisions of the sime firm when the

mbstihitibility among rival products h a s e s . Thus, a firmYr incentive to dmoonak

is reduœd if products axe M'tiated, d t i a g in an interior SPNE.

We then show that , if divisrone am allawed to divide fnrthex, they h a y u wiU The h d

outeorne of the divisionalization game rithout restriction on further dividing is equivalent

to the pafectly ampetitive e<iaiiibrium, wh- each fina earm w o pmfit. To priepent

thîs disaetmus outcome of total profit dissipation, patent îums have a uniiateral incentive

to zestrict th& divisions b m fartha dividing. This hding pmvides a t h d i c a l jus-

tification for a rather important assumption in the divisionIlliwation literattue that only

puent firms are allowed to set up independent divisions, and that divisions themdves

u e not. Veendorp (1991) show8 that parent firms delegate output deasiDns and the like

to th& divisions, but not invedmemt d&ns ïegatdhg dhhbns7 capadty. W e show

why patent firms reserve the aathoaitg tegarding the division~ation decision. Oor fmd-

ing is rlso consistent with the generd bmhess practiœ in franchising. Rmchisees am

asuaily not allowed to dl franchiees thexwelvea. An alternative otganizationd se&-up is

that the parent film QPctions aa a holdmg Company, &whg its eabmdi&s to manage

independently and, at the same t h e , taking away the authority of &t@ up subdivisions.

Fina&, we study the ened of divisionakation on the hee! d r y equilibriuxn. Becanse

en- induces incumbent h n s to se( op more divisions, aad the nombers of divisions

of firms are strate& complemmtr, entty un enormcdy intenrafp competition under

divisio&ation. An entrant kQcl cumpetition not only h m the h t b g divisions, but

.Ise b m dry-induœd additional divisions of incambent firins. As a d t , potential

nnnS are mon ductant to enter a market if divisionalbation ie possible. In 0 t h wordr,

dbbionalization ir a nafnral atzy burier, potentially generating high and persistent

profits hg the incumbent h. k the caties where producf difokm~tiaiion ia d i S d t ,

the only pare strategr free mtry SPNE is the monopoly outane. More intemdnglpi in

such Qrcnmstanœ~, it is the endi threat of divisionalizaticm a f k entq ocam that

e . the monopoly outeorne. The bcumbeut does not actiully have to set op divisions

prier to entry. Thie hding shsrply contrmtr to Eoton and Lipsey (1979, 1981), Gübert d Newberq (1982), and Schwartz and Thompmn (1986), who suggeat the iiicumbmt

firm har either to baild up capacities or to set etp divisiom priot to en* to pmrent it

dèctivdy honi happening.

The paper is closely related to, bat âistinct h m the m a g a litetatm such u Salant

et aL (1983) and Guidet and Salant (1991), which examine the impact of mesgers on

îÙms' profits and on social weliàre. Under pkiuible conditions, they ciha that mes- of

a mbaet of fians may tesult in profit los8 for the mer& iirms, even though nager leada

to a more conœnttated oligopo1y. This papa deala with the oppoaite issue: the incentive

fàcing i h s to divisionaliiteor to set up tivalindepenht d t r . We show th&, in plausible

soenarios, each firm haa diahad incentives to -te rivd cornpethg cinita. U d c e mod

of the merger literature, our d y s b permit8 one to analyze the eqoiliihrium consequemes

of these incentives in a noncoopetative setting that allows dl fÙms to divisionalize M y .

The rnager litadme, in contrait, implicitly vierr rnerga aa a cmoperative game smong

merging pa,rties, bor the set of h n s that metge L u d y exogeaoady deded.

The rest of the pape^ proœeds as bbws. Gi the next section, we set up the basic

model. Section 3 characterizes the eqdibzhm of the two stage dmrion.lieation game.

Section 4 considers the implication of the poeaibility of furthex àivisiondiaation by dm- sionil. Section 5 examines the h e en- eqoilibrinm. A final eion condudes.

3.2 The Mode1

3.2.1 Demand and Technology

We wnsidec an environment w k n oligopolistic Grms each produoes a Mken t i rkd

p d u d . To srniplifi the uialysis, demmds CDr dlnerent btandzi are asaumed to be repre-

aented by the bIlowi~g linw syrtem:

oDr k = 1,2, ..., n, whem d E (O, b), and 2, and pi, ate the copsomption and price of the kUL brnd tespectively. Notice that d can be viewed aa a puame- in di^^ the depm of

brand Mkrentiation (at the d e p e ofwbstitution between btads). As d appmadies zem,

brmds become more ~ ~ t i a t e d , and in the K t (d = O), danrnds axe indspendent.

AB d approaches b, brands become closer substitutes and, in the Mt, beaune p d d

mbstitates.

h order to isolate the atrategic motivation Qr îums to divieionalh, ne uciame th& oligopolistic ârmr have constant-rettun-bscrle technobgies with the rame maqinai a&

Then, nithout lors of gmeritg, we set the marginal mat eqad to zero. Further, &visions

of the crame parent firm ioberit the s.me technology. Thw, diviaions of the same fian

mpply paBect sabstitutes, anddiviaions of dihent fimus wpply im@d substitutes. By

eonst~~dion, the intraAk mbstitutobility is greoter thrn the inter-fizm substitutabillty.

TIiU kattue of OUI model wi l l be shown to be critical to enmirhg the mitence of an

interior SPNE. Mo~eover, divisionalization is aaiimed to be mstlees(i.e., the & . o n

setnp cost is zero). Honever, to enter the market, a îmm hm to hm a f k d mst, F, which cui be intapreted ur a R&D cost Lot depebping a product.

3.2.2 The Divisionalizat ion Game

FoIlowing the convention in the litetature3, ne reîèt to a firm setting ap auto~~moucr

r i d divisions as divisian~ation hereafter. The divieionabation game we consider is

a simultaneo~s-move two-stage game with paOed ipfiormation. In the fist stage, each

oligopoWic hm simultanwusly e h o o r s its namba of autonomous divisiona. In the

second stage, aU divisions engage in a Cournot cornpetition by s e t t h levele of output

simtaitaneody. Every market patücipant knowe the demuid stnictare and technologies.

Divisions can be viewed aa independent profit centers whose managers are eompensated

solely accordhg to divisions' profits. The profit of a parent 6rm ir the soni of the p d t a

of its divisions. We mlve the game by backwatd induction: mlvhg kat h r the Cournot

eqaik'bnum outputa in stage two h r a given set of numbers of dhhbns, then bt the

eqdi'briam nomba of dir ions chosen by each firm in stage one.

Notiœ that, like 0th- modela in the divisiondlsation literature, we implicjtly asnime

that autonomous didons wi l l not farfhez divide into more independent 8obdiPisions.

The analysis of divisionalization depends Cntically on this asaumption. W e wîIL ptovide

a theoretid justification h r this assumption in Section 3.4.

In thir section, n e fiet iolve the two stage mbgame perkd Naah eqdibrium by b&

r a d induction. Then ne discuss the comparative at&c r e d t r of the eqdibrinm and

mmmarize otrt main findinge.

3.3.1 The Second Stage Conrnot Quantity Game

In the second dage, ail independeat divisions choose their levele of output simulti~~~eoasly

h r a giveri set of nombats of divisions. Let rnk denote the number of divisions of &m k,

and zk be the output level of division i of km k, where i = 1,2, ..., rnk and k = 1,2, ..., n.

Subsaipfs k and i denote finn k and division i of ârm k, respactively. Notiœ that the

total output of the &th fkm zk = C(=2 zg. Then, the profit fnnction of division i of firm

k is

Diwion i of k m k chooaes Z& to maximize its profit, takhg the output deciaion8 of

the othet divisions as givem. The first order amdition yields

fot 9 k and i. Pure strategy Nash eqoih'brium is then detemhed by the above equation

systm. Solving for zk, we have

substitater and the degee of substitution haameu with r.

Notiœ that zi, is the saine Pot 9 i. Somining the above qation orer i fields

bDt dl k = 1,2, ..., n. Equation (3.5) i n m i . only the totai output of each hm and, thas,

can be viewed as the beet reiponse fanction at the fkm hrel. Solving xh in terme of the

numbets of divisions ,we have a&

Lemma 9.1 : Gien the Iinear denund system, hr each o o ~ a t i o n of numbers of dm- sions of the oligopoliatic - ml, ml, ..., %, t h e exists a unique Nash eqdibnum

in the Coumot quanti@ gune. Momover,

(a) a division's output decreaees with the namber of divisions of each h;

@) a parent h ' s total output bueaaes rith itr niimber of dipigioau and decre-

with the number of diWna of evexy othet firm; aad

(c) outputs of every division and ficm deaeatie rith the n u m k of finni.

(Proof: see Appendk 3.)

The &Ag hrœ behind Lemina 3.1 is that divisions' oatputs are strategic substitutes

in the Coumot game.

Define the market ahare of hm k as the ratio of itr output to the total output of the

industtg: q = I, where z = xk. An intezesting c010Jlary of Lemma 3.l(b) is in

order:

Cotollary 3.1: An iacrease in the namba of divisiom of one firm hczeases the market

share of th& fitm aad deenases th& of e*ay otha b.

Comlhq 3.1 highlights a h ' s pPIRte incentive to set op competing divisions. The dual eftkcts of divisionalizstion on a firm's p d t csn 8bo be e d y h h m the hL 10- derivation.

Reaxrmging equation (3.3) and oshg the inveirse demand bction gets

S i n œ zfi is the same br d i , the profit of nmi & can be d t e n aa

where & = 21qi8& < O. The Gtst tenn of the above eqoation rep-ts the dl& of

ueating a new division on the profit of the exkithg divisions of the ftm. We shaIl& to

this &ed ar, the competition dèct of dmaonalization, &ce the new division incresses

the levd of competition and teduces profit8 of the exidhg divisinne. The wmnd krm

represents the direct contribution of the new division towasds the profit of the fum, We

$hall t e k to it as the bnsiness stealing deet of dmeionalization, &ce the output of the new division comes partly at the met of otha bu?. The second dect highlighti the motivation be!hînd divisionabat ion.

3.3.2 The First Stage Game

Given the chatacterizdion of the eqdibrium in the second stage, ne a m consider h n s '

divisiondiaation deQsions in the fit stage. The parent fitm k's totai profit is the sum of

p d t e of aJl itr divisions. Then,

Fiun k ehooser na& to rnaximize its profit taking aa given the namber

divieionS. We have the hbwing 6rst or& condition:

(3.7)

of other firmi'

whexe k = 1,2, ..., n and Ak = ze 4. Eqyation (3.8) defines the eqydiiria of the flirt

stage divisionabtion gaane?

4The -ad orda derivative eduating at the solution of the fiat orda condition is

Lemma 3.2 : The numbers of divisions of the oligopoüatic firmr ue dta,tegic cornpie-

ments.

Proot. Reammging eqyation ( 3 4 , n e have the bad respoxue fnnction of firm k

Lemma 3.2 implies th& a fkm responds to an in- in the nnmba of divisions of anothet km by incrtasing the namba of its own divisio~u. In doing so, a fum attempts

to mitigde its market ahare bas due to 0th- finne' allgersivenesr in divbbn.üsation.

Because the complementarity shorn hem ïmplies a positive chUn reaction among the

niimbers of divisions of f h s , a change in a fadot which aE&s a firm's niinrbet of

divisions might have a prodoMd effect on the number of total divisions and, in tatn,

on the levd of cornpetition. It wi l l be ahown latex th& thb inaight wi l l have signiîtcamt

implications on the en* deteflte~œ pro- of divisionalization.

hposing a symmefry condition to the equation (3.8)'' we obtain the m1ution br the

equilibriam numbet of divisions m:

Propodtion 9.1: With hear danand uid dinerentiated produdi, the two stage dm-

&nakation game hm a miqne mbgame pe&d Nash eqailibrium, in which each

firm chooses a finite nnmber of independeat divisions. Fbtkmore, the egP3ibrium

numba of divieions of each fmn increases with the degree of substitution between

produds and the number of fitmr (the namba of differeatiakd productr).

Proof: see Appandix 3.

Proposition 3.1 ststes that p d u c t diSetentiation enimnr the e308teace of an interior

SPNE for the divisionalhation game. The dect of produd dinixentiation on the deta-

mination of the eqrii1ibriu.m number of divisions is esident h m the positive relatiodp

between the eqnilibrium numberof divisions and the degres of substitution between &nu.

As we have shown ealier, divislonalization enables a fUm to steal business h m its rivah,

on one hand, end mates cornpetition br the f i ' s existing divisions, on the other. The

business stealing eflect decreasa with the degree of diBerentiation among pmducts, rince

lower substitutability amomg producta nattlltally limits the hm's ability to shift the de-

mand h m its rivale' productri to its own product. The cornpetition &&, on the mnttary,

inueases with the degree of pmdud differentiation, because additional divisions have to

compete mainly with the exista divisions of the same hm when product stibstitutability

is bw. Thus, fmnd incentive to divisionaIize is reduced when produds are difterentiated,

resulting in aa i n t d SPNE.

The existence result of interior SPNE aith producf dii€&entiation can be k 1 y iJlak

trated with the hdp of equation (3.9), the best response hdion of fi= k. With product

Me~entiation, Le., z < 1,

Then, if f h t in=- its n d e r of divisions, m, h k hur an incentive to in-

its nombez of division8 but riU not match the inaease in m. Mozeover, as + 00, l + n 2 - + O andrnt +,* 5 &. RedbmLernnia3.2thatmkm-

k t

with m. Thur, the beat respowe fooction of k m k is b o d above. No matta hor many dipisions 0th- firnu set op, fum k dl not set ap mon than & dhhbns. Th& gn~~anteea the interior equilibrim.

Without pioduct dikentiakion (z = l), however, eqiution (39) beaunes

and

That is, firm k has an incentive to match any intlfe~~~e in the nnmher of divisions of any

other h. Tke ia no upper bound hr the best response fandion mk. In a, each

firm h a an inœntive to set up more divhbns than the nomber of divisions of dl the othn

fuma combined. That dmee the eqdibrinm number of divisions to infiaity.

In the case of duopoly, the two best response fundiions con be pbtted in a diagzam.

m e n z = 1, they are two p a d k l lines (F'igure 3.1 (a)). One always lies above, and the

other lies under the 45 degne line. No interioz eqyilibrinm exists. When z < 1, howetm,

the best response m e s both bend towuh the 45 degree lins md are bonnd above at

(see Figure! 3.1 (b)), nsuiting in an interior ecpilibriam with the number of divisiom 1-2

for each firm less than &. It is worth considdg two extxeme aies. I£ th- is zero mbstitiition iutiong pxod-

ucte, each firm kaa totdy independent markets. DivisionaIization then &es the

ampetition dect, but not the business st&g effect. Thus, the 6nn has no incentive

to divisionalize. I£ producta axe @ct substitutes, howeeet, the business stealing & '

P at itr maximum and the cornpetition ened is at itr minimum6. In bd, the hrmer

alrrays dominates the Mer . Each finil in eqoiabriiam wil l up infinite divisiops. We e i immh these two cases in the hbwing c~milariea:

Coroiiary 3.2: If t h e is sero scibstitution amoag prodncts, fmns do not division^.

Corollary 3.3: If oligopolisf~ produœ @d mbetitutea, the eqdibrinm nlimber of

diviaions h r each fixm is ;nfin;ty.

ComiiPrp 3.3 is one of the main msults of Cachon (1991), Corchon and G o n z k

MPestte (1993), Po- (1992), and Bap, C d e r and Jo (1995), who ail conaide a

model of homogeneous pmducts. Oot d t s show that the nonexisteme problem in the

p d o u a stadier is mainly due to the assumption th& finnr mpply homogelleu08 pduct i .

Produd differeatiation automatically guarmtees am intezim SPNE.

Pmpomtion 3.1 dao diarachhm a positive nlationship between the eqiiiübtium nom-

ber of divisions and the namba of dikentiated produdr. Th& k, firmr get more ag-

gresmve in divisionalhation when they face more competing &mr. The intuition is th&

the largex the numbet of cornpethg firms, the mom sources a firm can steal buaineu h m

and s p d the additional cornpetition to. Comeqaently, firms have s hi&a incentive

to divisionalilce and, as a result, the e<iaiÜbriom numbet of dhhbns of e h firm fl be

higha. This r d t .Is6 h a a sipifmat implication hr en* detemmœ. It implies th&

an entrant haa to compete not OJ& with the divîsbps existing p h to entry, but aie

with addition$ dh6shns hdnced by the entry. We d carna back to this iasue in section

3.5.

3.4 Possibility of Furt her Divisionalhat ion

In the two stage divisionalbation giune, we impliatly ormme that the original puent finne

cui eet up divisions, but divisions t h e d v e s cannot. What happens if this aasumption

is relaxed? WiU divisions then hrther divide? Will parent h n s ' profits decreaae or

in-? Do parent finns ha- incentim to restrict divisions anilaferally h m farther

dividing ?

To anmer thaie questions, consider a case where divisions are allowed to divide for-

tha into autonornoos aubdivisinns. Let a division's profit be the sum of profits of its

subdivisions. We wi l l fùd show by ûontradictio~~ that if divisions an dbwed to divide

fiutha, they dways wilL

Assume th& th- e x b t s PO e q d i ' b h etriicture such that no dmrionr &ose to

divide fmther evea though they are frre to do m. Let mk be the numbet of divisions

of h k in equilibrium, whae k = 1,2, ..., n. By dedinition, it is not pmfitabk hr aay

division to divide fartha in eqaih'brium. Now, imagine O hypothetical -ha b d p of

&visions. Let SE be the number of independent nibdivisio~ in dmsion i of finil k. The

totd number of diviaions of firm k wi l l be Nk = z:dh skj. Acootding to eqoaticm (3.?),

the total profit of iirm k M

Then, the total profit of the sfi subdivisions of division i of fum k k

Division i of fitm k chooses to maximim FM taking the namber of stibdiviaiops of otha

divisions as given. After s i m p m g the fùst order condition, we have

Notice that z:~' akj + 1 is the rider of subdivisions ditrision i of 6tm k wodd set up

if there were no other kms besidee k, and ,* is the number of divisions induced

by the d e n c e of mbdivisions of films 0th- thu, k. For m, 2 2, the symmetric

solution to the above eqtution is infinity, which is not suxprising, shœ dh%ons of the

rame îum snpply ped& mbstituta, and, t h d r e , the business stcdmg efEèct dominates

the cornpetition &èct in furthet divuion&ation. This remlt obviously a>ntradicts oiu

aammption eulier that there existe an eqoilibrium struchm in which no divieions ha=

the incentive to divide Qrther. Thus, if divisions axe ailowed to M e Wher, they dways

Wiu

Ftufhermore, the total profit of the firm WU does not &ricf ite divisions 6rom

fiutha dividing is

.nd the pria of

That is, abwing divisions to divide fiutha leads to &ero markup and m m p d t 6Dr the b. The d t holda reg&tdk~ of whetha othet h~ a b w th& divisions k, M d e

fartha. In orda to avoid the total dissipation of profit, each hm has an inantive

to d c t iti divisions unilattxdy from farfher dividing. When a pmmt fmm casinot

& d d y &rœ this restriction, it t better not to set op divisions. The d t r axe

sammd as mow8:

Propoiition 3.2: If divisions of a firm axe allowed to divide fitrther, they ahraya wiU,

teeulting in total-profit dissipation Qr the pasent hn. Thus, each firm has an

incentive to testrict ifs divisions uniiaterally h m fiutha dipidimg.

Ope implicit but c t i t id asaumption in the kategic divisionakation litetafrue is th&

ody the paient firms can set up divisions, and the dkbbns t h d v e e ca,nnot. Withoot

this aummption, the conespondhg malyeis and xedts do not hold. Proposition 3.2 p m

vides a theoretical justification for this &ssof~ption. This remlt complements Veendorp'r

(1991) fmdmg that a hm in a mdtidivisb~al structure delegates to itcr divisions deci-

sions regarding output and the k, but resemes br i t d investment deciaion8 regarchg

capdties. We show that a patent fitm wiU m e the divisionabation decision. l'bis

finding h abo consident with the genexal ptactiœ in tan- where franchjsees are

asudlg not allowed to set up k~anchims t h d v e s .

3.5 Free entry equilibrium

In this section, ne torn oar attention to the free ent y eqoübrirun. F o d y , we consider

the Qiiowing simultan8ous entry game with a large nomba of identical potential firniil in

the market:

Stage O: Firme make their entq decisiou given the other firms' entry decisions.

Stage 1: Fllme which have decided to enta the market in the hd ~trge choose th& numbezs of independent divisions.

Stage 2: All the divisions engage in Cournot cornpetition.

Notice that the iast two s t q e s of the k e en- game are the rame u the two stage

ditrieiondization game ne have aolved in Section 3.3. Th-, we oily need to d m the

entry gazne in stage O.

Fhe entry, by dedinition, e n t a sem proM lot each iùm in the market. That F, in

the entry eqailbrium,

r & - F = 0 ,

or,

where m is the solution to equation (3.10), F is the fixed cod asmurted with entrp, and

r h is the goss profit of firm k. Eqaation (3.11) d&es the number of finru in the &ee

entzy e<ioiiibBum.

Proposition 3.3 For a gken F, thae m s t s a pon strategy SPNE b r the fres entxy

game. Mozeova, the equili'brium number of finns (or difkentiated p~oductÙ) d e

mases wïth the degree of substitution between the produda, as r d as with the

k e d entry a>&, F.

Similot to Sdop (1979), ne find that, in eqyüibrium, the number of ie negatively

related to the magnitude of the h d en- cost. Howetrer, our results imply a mach

otronget case fbr the persiatence of high profits (except the case w h n the zero profit

condition prodaœs an exact integex solution h r the numbes of f b s ) . Since the eqoilib-

riam numba of divisions of a fmn in-8 with the number of fmu, the cornpetition an

entrmt faces corner not only fion incumbents' existing divisions, but diio h m additionai

divisions hduced by d r y . The n a m k of additional divisions indoced by entry can be

ratha luge, due to the complementarity among the numbers of divisions of diffkent

f b s 7 . Thns, entry might induœ vay sevexe ampetition and ptodit disripath. h a

d t , with division&ation, a potential fum is mer% ductant to enter the mrtket, and

the incumbento may, in tum, enjoy abnomally high p d t s (thU L &uly illastrated in

the bIlotffiPg example).

Lilte divieionaliaaücw it* the mtry detemznœ &ixt of divisioniuüsation in-

with the degree of substitution among pmductr. Aa z appmaches 1, even a doopoly rill generate ao manp divisàom thah the last stage Coumot game wiilgenerate an outcome dore

to the paOectly cornpetifive egdibrium. Then, the only pomible fke enky eqnilbriom

k the monopoly outcorne, even if the en- cod P relatively lor. Consequently, the

incambent con persistently esni the mompo1y p d t , whichmay be maay times mon than

the en@ a>&, without wo-g about en*. For example, in the case of a dnopoly (n =

2), rn = ,/&A' (hm eqgation (3.10)) and the profit of a duopoliet r = tir+&1--& from (equation (11)). When x = .98, rn = 5, a duopolist's profit is 8.4% of th& of a

monopoly, which is S. Hmce, if F, the h d en- c d , ie g n a h than or equd to 8.4%

of the monopoly profit, the fme entry eqaih'brium is a monopoiy out come, despite the fod

that the monopoly may eanr as ma& as 12 thea of the entrp a>&.

It ir worth noting that, in this case, it is m d y the threat of divisionaiization (not the f b d entry cost) that causes the natutai monopoly outcorne. kiteresti;ngly, m U e what

the previow fiterature hm mggeste#, divisionalbation does not need to occur to asmue

the monopoly t e d t . The credile threat of divisionfiation in case! of entrg M enough.

The above redt b 8 0 n u 1 l d in the fobwiq proposition:

Proporltion 3.4: Under divisionalization, incumbents in fke entry eqdibrium may per-

sbtatly eam abnomally high profits. In particular, hr auy given F, there exista

a z* < 1 such that, fix any z > x*, a naturd monopoly b the nniqye pure strategr

h e entry SPNE, nhere z' satisfies irF& -a = F$.

Remuk: There ie a patadoxical impJicakion of Proposition 3.4. Given the numbet of

Gnne in the industry, divkiona,lization i n t d e s the levelaf competition and alleviates the

distortion in pricing. It saans that, h m a social point of view, divisionalbation iihould

be encouraged. Under k e en-, however, the t b t of dmsiondbation by hcumbents

redtaœs potentid entrante' incentive to enta a market. The competition levelin free eatry

equiJibrium with dioisionalization might be mach bwet tham when no divisiona,üz.tion b

dbwedg. In siunmary, eren though Mtmg the nclmber of autonomous divbiona of fitms

may weaken competition in the shozt mn, it un shqgthen competition in the long ru.

@For exampie, Schnuts a d Thompuon (1986) show h m the iPeombant bottdt4nd d r y by set- tip

iadepenàent divieiona just prior to the date of a poteiria cotry. % the example whcre s = 98, if F L 8.4% of the mnopoiy profit, the k e enhy eqdibtium 6 th

dianJirCrtion ie mompoly. If divigandirstioti iIi no4 ulbwed, if is mwy to v d & that t h e bc at

In thh paper, wa consides an environment in which competing oligopolisfic &nu with

d h t i a t e d producta am set up indepemdmt rival dipisions. We mdyze the str.tegic

inantimi fbt a fiim to divisionulisa, charackhe the eqaih'bh of a dIoision~ation

game end highlight the dect of p d u c t di&ereati.tion in enmuhg an intexior e<ioiiibrinni.

By allowing BDr pdrrct àifEèxentiation, we demonstxate th& the existence of an htetiot

eqaitirium ca,n be achieved without relianœ on ad hoc assumptions, mch aa an exogeno~~

boaad of permism%le rider of divbhns or a eostly divisionalbation.

The existence of an inthor eqirihirium depends heavily on the asmmption th& di- visions of the same firm pmdaœ closer substitutes than divisions of diikent firms do.

However, the divisionalbation r e d t does not depend on thir ammption. Whea $1 fimu

produœ homogeneous produds (the modd of Corchon, Po- and Baye et al.), fiaiu

still divisionalize. In tact, they set ap an infinite numbe~ of divisions iu eqailibntlpl. We

can infer that, if divisions of the rame firm are able to be difterentiated mch that division8

of Merent firms produœ ciosex mbstitutes th- divisions of the same h l o , the business

stuüng &ect d be strengthened, and the cornpetition dect wi l l be w e h e d . Thar,

fitmr wotiid have stronger incentives to divieionalize. Aemmhg thae is no b d set-up

met, each fùm wodd set up as many mch dinerentiated divisions as possible!. However,

difterentiation of divisions of the rame h n often re+ diflimntiated products, and dif- h t i a t e d products oftm imply R k D eostr. In such cases, according to Baye, Crocka

and Ju (1996), fixed &op conte may limit the niiniba of divisions of a hm.

To isolate the strategic aspect of division.üsation, ne dso assume a coPBf80t retum to

sc$a technology. Yet, the natue of technologies is an important factor when finns chooae

the namber of divisiom. Increasing retotn to e u d e technologies shodd teduce firms' in-

centives to dmsion.liee (dividing produdion), and decreuiig return to r d technologies

shodd inmeaie mch incentives. For example, the in- mtum of ecale natue of ad-

vtzthhg in the œreal industy mry pteoent d fùms h m setting up Werentiakd

dmeionr even though erdi caed hm h u a numba of diflezentiated pmdudr.

We &O conader the a>nseqgenm of OIbwing diviaions to dmds farther. It i hund

th&, if divisiom an allowed to divide fiuther, they always wilL Then, the only pokbk

outcorne is the one in which the fùm th& ailows its dhkbns to divide fartha haa aa

W t e numba of dmriom and zao profit. H e m , each fism haa an inœntire to re&ict itr

divieions nnilrrtaally h m fiutha bseakup. Oiu fiadin,g provides a theodical justification

ht the assumption in the strategic divisiontilization litastora th& onlJ puent ârmcl crra

set up divhiom, and divisir,~ th=&= <.annot.

Finally, we d i e ~ t l ~ ~ the free emtry h u e . We h d th& diWnaJjzation hm a nstnrai

entry det-ce property, for it can sigdcantly magiig the severities of compatition

in the tPae of entry. As a result, incnmbent finnr may pezaisteatb eam abnonnally high profite in dree entry eqyilibrium, relative to the no divithnalization case. Li fact, when

6inne have difficulty Mkmtiating h m each 0th- because of eithet the conœntration of

consumera' tastes or technologid reu*ms, the ody pure strategy mbgame met k e

entry eqdibrifllp is the monopoly outame, even if the entrp mat b relativdy low. By limitiag the nPmba of independent dipieione or fiancùks, regdators un &udy help to inaease cornpetition. In addition, in contra& to the previous literattllte which mggestrr

that the incumbent actually haa to set up divisions to deter entry, we show that the tlueat

to divisianalize may be enough to aisiira the monopoly outawie. Considering that the

eqnilibrium we aiialyze is r h e en- SPNE, this result is rather mzprining.

Chapter 4

Divide and Conquer: Strategic

Leasing in Common Pool Oil Fields

"The o v e r e g that haa taken place ... represents s tremadous economic

rade, not only in the expenditnre of capital, but in the dUBpation of natorral

reiiouras." "The overdevelopmed m o t be said to be entirely the faaU of

the operator, 60r the londowner i~ equdy to blame." pulletin of the Amcrican

Aaaociation of P e h l e w n Geologisb, Vol. VILI, JJulyAugwt, 1 sa]

4.1 Introduction

Sina petroletm waa first Lund in the U. S. in the middle of the 19th centuy, oil p m

dudion has b a n plagued by serious conunon pool wastesl. They are umally attniuted

to exœsmve ddling, u n n e ~ e 8 s a y a d i m stotage, ovezd~action, and reduaed altimate

oil recovery. Under the cornmon law rnle of capture, the pmperty w t s to oil an ody

usigned upon extraction. When multiple compete ht migratory oil in a cornmon

pool regervoir, each hm an incentive to dPIl competitively and drain oil b m its neigh-

bors. Common pool b86es arUe as capital costs .re &en up by the ddling of excesaive

numbera of wells (more thra geologic and flaid conditions wammt) and the consttoction

lForemmple, in 1914, t h US. Btiiaao of lYfiig atimitod mnuallœmes heompstit ive uhrtion at

(60 millbn, appninmstcly owquwbr of the total d u e of us. pdiicfian; the kderal OP CoMervation Borrd (1926, PM; 1929, p.10) aatimJed mmnmy r . t a d d y 20-26 percent nith canpetitive &action,

w h b 8590 pezcent waa paiible with eontroûed rithdrawd.

of surfaœ etorage. Rapid production .bo pranatdy deplefes the mbmrkQ pmslmn

and in tum redaeer the total reeovety.

Ghen the extrmrdinsry costr of competitive proàuction in common pool fiddr, one

wodd expect th& lsndowners have inantim to limit the niirmber of independent oper-

atora in order to =duce the mmmon pool lou &aked with competitive extraction.

Howevet, a wide s p d phenomenon in onnhnte oil production in ht hdowners in the

iame oil fi& O&= divide theV hdh01dmg into m d k pieces and gant pdodion

rightr to multiple difterent operatort?(a phenornenom I hall leder to as multiple I d ~ g

hereafkx). Landowners' multiple leasing practiœ can aerioarip aggravate the common

pool probiem. Givea the competitive behavior of independent operators, why doer a

hdowner gant more than one le-? This papa attempts a game themetic explmation

to this puzzling phenomenon.

Table 4.1 (see Appendix 42) s a m m h the laadholding and leasing inhrmation of

the 42 U.S. onshore oil fidda, which 1 collecteci h m mery amd Southweat oil production

maps in variom issues of Oil Weekly6rom Febmsry 1938 to Aptil1940. Colnmns 2-4 are

the number of laadownm, the number of independent operators, and the number of leases

in each fidd respectivelf. The fifth mlumn ia the tatio of the namba of operators to the

numbet of landornem. The last dumn b the average number of leaser p a landownes.

In tame of leases, Table 1 ahons th&, in all oil fidds sampled, leanes are mon numerous

than laadownere. In 36 out of the 42 fields (or 86%), there axe at lead t r i a as many

leases as landownenr. Averaging aaoss fields, each lsndowner has 3.8 leues. In terms of

independent operators, nimllaz d t r p e r d : 35 out of the 42 (or 83%) oil fiddr ~ampled

have more opesators than landowners, and the average operator-1aadowfle.t ratio acmsi

f i e ' i~ 2.6. The field b e l data shows th.( multiple leasing is a rather widespread ptactice

in the e d y stage of U.S. onshore oïl fields development.

FotmaUy, we view that the oil ndd development consista of two stages. In the finit

stage, the landownem sirnultaneoudg choose leasing strategies. In the eeowd stage, in-

dependent le- operators p&œ oii oornpetitively by choosiiy extzaction hategies

simdtaueously. Not g~~p&i&y, it is kund th& cornpetitive &action by multiple in-

% the rample Likap a d W w (1984) uaiiblai, bPr emmpb, Y& Bald hr 16 Mepi?ntlant

opetatom but ody 2 initialandownm and H& fidd hm 18 operatas bot d y 3 luiAarnem. S t i w m e e a a , ~ o p r a f o r o n n r ~ ~ m a L e u a k o a f h l d w t h i t ~ e n n i i m b a r a f ~ ~ y

diSr h m that of opuibn . Th& ir rhy data on both of them are p d .

dependent opezators hade to ovaddhg , overextractjon, and d u œ d recoveqr. Mon

importuitly, it is ehown that, in a nonexcldvdy o d oil Md, it ir individualiy rc

tional %or a landowner to subdivide his ladholding oiiilaterally and delegate pdaction

rightr to mdtiple independent lease opaato~r. Conseqyently, the production kue own-

etship is umdy more dirperd than the landowndp. L a n d ~ ~ ~ ~ l e i s iue as resp~nsibie

aa the opaatora Qr the sezious a>mm<w pool nades.

Giren that l m concentration of production I d to more m*ous rent dissipation in

a eoxnmon pool, it seans irrational fbr a landowner to grent leaeee to multiple operators.

The key to understanding this paaale is that operators of a rnulti-le88e h h e r as a

whole are more agpasive in oil production than the Isndowner. This is because they

ignore the extemality of their extracfion on each otha, in addition to that on operators

of 0th- Isndowners. Eswntially, the multiple U g rtrafegy enables a h h e x to

behave as a Stdebexg leades and credkbly commit to a hyha production level and, in

ttun, captures a bigger shsre of the aggregate output and of the fiddwide eccmomic rent.

Multiple leasing decseases the fieldwide r a t , but in- the hdowner's share. Tb effect of the hcreasing shate can dominate that of the deaeasiiig total rent. The tradeoff

of these two dècts detexmines how maay leases a hdowner d p a t .

Unfortunately fat the kadowners, if they aJl b b w the same sttategy, everyone wil l be

nome off in equiliirinm, h r multiple leaaing inc~easea the exfzaction rate and, therehre,

the cornmon pool bsses, but Isadowners' shetes of output (or rent) rempin anchanged in

eflbrium. Nonetheless, in the non-caperative game, given other laudowners' stratepies,

a l~pdowner hair to piirsue the multiple leasing strategy. ûtherrise, the iaudowner wi l i

do even worae, h r it wïl l captiue a smallex share of the ahtunk total output aad rent.

This papa is d o d y related to, but distinct hm, the cornmon pmpaty litetatm.

Much of the common propertr literature (Gordeo, 1954; Hudm, 1968; aiid Dasgapta aad

Hd, 1979, hr examples) focuses attention on the economic waates undet ampetitive

production, but not on the dete.tmination of the organizaticm of produdion i t d In thia literatiire, zemuxce ownm u e umally impliutly .ssiuiiad to be the rame u nmofce

develope~s, and thus the pro- ornenhip structure is the same as the nsoora oper-

ation etnictm. The traditional a p p m d baves the choioes of ini?iiin'ent otganhation of

production uexplained. The main haa of OUI analysb is the drategic choias of the

organization of production by pmpezty ownm (hdowners). Mon p d y , we show

that hdownete have ineenti- to delegate production rightr to muitiph indepenbt

operators. As a result, the kndownership stracture is, in generol, dine~e~t h m the pro-

duction operation stracture. Themhre, the traditional theoy tenàs to andet-eatimate

the tragedy of the ~0333333ons, if tesoo~ce ownerehip structure is ased aa an apptaxbate of

the operation skiictuxe.

This aaaly& is .Ira related to the literatare on stsategic division.lieation in Cournot

cornpetition setting. Many authors, Corchon (1991), Polasky (1992), and Baye, C h

and Ju (1996), kr examph, andyze a two dage divisionalizafion game. In the gazne,

pereat fitms chooee the numbex of indepeadently msiiaged diviaions in the iùst stage,

and dioisions compete in a Coontot kshion in the seamd dage. It is ahown that each

firm hm an incentive to set up rival divisions. Tbis shows that a parabî argument can

be conetructed to explain a long aad puzzling phmornenon (multiple leasing) in oil field

dmehpment and organization of production.

The chapta pioceede aa follons. Section 4.2 pmvides o brief review of oil production

techno10gy. Section 4.3 presents a mode1 of oil fidd developmat. Section 4.4 pmvides

an analysis of laadowners' stxategic leasing behaviots in a conunon pool. Section 4.5

4.2 Oil Extraction Technology in a Comrnon Pool

In this d o n , n e &eass oil prodtrction in a cornmon pool based on models of oil extra^

tion teviewed and developed by Ben-Zvi (1985).

To rimplay the riulysis, we assume th& sn oil fidd co&s of a pezbedly-mnneded

aommcm pool without the stratification and sepuating kdts. Thui, theoil con potentidly

flow to any corner of the field. Withoat a h b t , this L aa ovessimpliîication of the d t y

but it captutes the essence of the annmon pool pmblem.

4.2.1 The ExtractionRate

Oil mmvoirr M umdlJ eompmsed between a loyer of naturat gas and a hyo of rater.

The underground pressme dtives the oil to the eatkQ when the mrrounm hrmation

is puncttl~ed by wells. The instantaneuus exftadbn rate depende on the geologîcal and 0uid puameters of the m o i r hirmation and the niimbat ofwellr in the field. Givm the

geological and fluid chara,ctetistics of an oil feservoir, the exfraction rate LDr the pool is

ptopoztiond to the M i c e between the wellhead p m r t e and the unkgrotand preumn

and is a concave function in the ntimber of wells. Thak is,

wheze q( t ) is the instrntaneous adradion rate; rj is a pstameter which measmes the e l k t

of geulogid and flaid characteristics of the re-oir; N is the nambet of w e h in the field and @(N) ir a concave fimction in N At) is the unkground presstue; and f i (t) 2 0 is

the wellhead ptesstl~e.

Theoretidy, opexatois ua contml the extraction rate by choohg ~ ( t ) . Since we

u e m d y interested in eonipetitive production, we uisume that wells produce at fd

capacity, Le., h ( t ) = O. To &pi& the analysie, we ailla aumme that @(N) = ~ i , wh-

d > 1 approximates the degree of ancavity of the initantaneous pduction fandion with

respect to the rider of web. The extraction fnndion then becornes

4.2.2 The Pressure Deplet ion Dynamics

U&e many 0th- exhaudibh natard resotmes, the ultinürte retx,very of oil depends

on the time path of output. With a high &action rate, the ratio of natural gm und watet to oïl ptoduced increases, le* to ptemattue los8 in mbsarka preamre. Due to

the 108s of pïeseore, the natard gas diesalved in the oil h v e s the soltltion, redoQng the

oil's mobility and leaving eigpificant remmes petmsnently trapped. It i~ veq costly to

artrad oil once the piessure h dauated. Henœ, chu-g the behavior of dt) U

an important issue in oil production. The rate of change in dt) is generally believed to

be a fandion of both the extraction rate, q(t) , and the presmre, At). Foilowing Ben-Zvi

(1985), we adopt the bbniiip fanctional hrm h r the rate of change in p(t):

where de t the rate of pressate depletion; a is a anstant; and b (a + 2 > b > 1)

55

meamma the degee of the convexity of the rate of p r a m n depietion in temm of the

extraction rate, where o > O. Notiœ that t h fundional k m implies that there is no

praumre depletion if no oil is extract4 othemise, the premmre decline~. Morarm, the

marginal ptessure Iws iaaeores with the extraction rate.

4.2.3 The Ultimate Recoverg

The ultimate recovery is dehed as

whese Q h the ultimate mooexy. Solving 6Dr dt in equation (4.3) y i e h

Substituting equations (42) and (4.5) into ( 4 4 , we have

0 ta b-1 n h a e ~ = ? $ ~ , a o d s = ~ .

Equotion (4.6) shows that the dtimate recovery declines with the total n u m k of

producing wells in a common pooL When th- O only one w d (N = l), the nltimate

recovery reaches ifs maximum, wheae Q = U. Thus, U is the maximum reeoverable oil

remme. The decliae tate of the dtimate reavery is m e d by s, which we rhall nCa

to am the gmss tent dissipation rate (GRDR). GRDR chatbcterizee how fast the gous

tent j d t h a k ncoveq) ii-asea with the namba of w&. Notiœ that, when s = O

(ot b = l), the ultimate reeoveqr is independent of the nomber of welb. The Fedetd

Oil Conservation Board (1926, p.30; 1929, p.10) estimotad th& the d h t e na>va~r

at ampetitive extraction is about 30% of that under contmlled withdrawal. Since the nMPbet of w& under cornpetitive exttactjDn ia umaly many times pater than that

undex wntroIled withdrawal, it can be infernd that s ir a nrimba between aao and one,

ond perhaps reiafively close to wto. We th& asmune hexedk th& O 5 s c 1.

4.3 Analysis of Compet it ive Oil Extract ion

In t b aection, ne uialyze the eq@ibtmm of wmpetitive exfraction of multiple indepen-

de& operators in a common pool oil fia. Li orda to Smnplify the d y s i s , the hbwing ammptiona axe made:

Al: The d d h g cod functi~n is 8cummed to be D(N) = NC, where C denoter the

maxginal mst of drilüng a well, and D ir the total d d b g cod.

A2: The crude oil matket ia assumed to be perkctly cornpetitive. Withoot the lors

of generality, we m e r asaume the aade oil price to be oonstsnt over t h e ruid normalize it to be one?

A3: The discount rate is asanmed to be zero.

Uwdy, ddling mat is a s m e d to be pmpcntional to the drilJing depth. In assumption

Al, 1 implicitly Bssume that al l wells in the same oil field have the iame depth. My

justification for it is that, b e k e d d h g occurs, the relevant chihg cost br potentid

lessees is the expected d u e , which ir more or k a the rame in the same fi& Aseamption A2 is aot weasonable. First, in addition to numemas world oil produe

err, there are in the U.S. alone thoiuiands of oil fielde and many thes more independent

opexating hns . Thus, oil produœrs in a rekively small oil pool fa^ an approximately

mmpetitive muket, des s they mably mpply ht a datively indepadent local market.

Second, in making leasing decisions, the relevant oil price is the expected btifure pice. It

ir not unrommon to assume the expected oil priœ to be constaat in the fattue.

Asmption A3 L obviody an oversimplificatbn of d t y . Eowevcx, it hdps to

make a tedious dexivation tractable. Under a zero discount tate, the present value of oii

production becornes the ultimate ncovtq. A nonmm discount rate does not a&ect the

main d t r of the paper but only complicates the deEvatkn.

Conrider a simple setting, wheze L independent opaatom extract oil competitinly

in a coinmon pool oü field. More speafically, we conaider a game where L operators

choose th& extraction strategy eirnaltaneously. Smce ddling is eostly, each weU ddled

wil l prodace to its n9 capacity. Sinœ we BSSume that an oil field conrkts of a pexkctly-

conneded homogeneous a>mmon p l without the rtratification and qarating fatits,

the oil can M y flow to any mmer of the field, uid the geological conditions are rame

bot e d well. T h d r e , each rd dl produœ at the rame capacity. Thas, a0 operator's

extraction strategies are h p l y chootïhg the ntmbet of w&.

Let Ni be the rider of welb that operator 1 ch-- to d d , whem l = 1,2, ..., L. The totd number of wells in the comnon pool is N = fi . Sinœ sach well pmduosr

at the same rate, operata 1's output abare and instrntaneous ext18CfjOn rate ue then

# aad gq(t), respectively, whete q( t ) is the totd jnstantuiamt extraction rate in the

common pool. Operator 2% net retum h the pra~nt value of its revenue flow, minus the

drillhg CO& and the ked lease k, A, th& is

Taking as @en other operators' number of web, operator 1 chooses Ni to r n a x h h

bis net retani. The first order condition fields

On the left-hdaide of the above equation, each of the three ternui repreaents a

dinerat e$& of d d b g an extra w d on operator 1's profit: the Gst tean meatmes

the gain due to the mbaequent increase in operator 1's output share; the s e ~ ~ n d term

meastues the bss due to the de- in dtimate mxovery; and the thad term meatmes

the 108s due to the increased d d h g a>&. The fùst order condition deuai'bes the date where these t h eS&s are balanceci.

M t i n g equation (3.8)' we have

Notiœ that the Nl that solve8 equation (4.9) is independent of the mbacxipt Z. That is,

NI b the same bt 1 = 1,2, ..., Le Denote the equilibrinm nomber of w e b pa opaatot by

n. Thm, the number of wells in the field is N = nL. Moltiplying equation (4.9) by L and solving h r N, n e have

h r L > s + 1, where c = 8 is the ielstive marginal drilling a>& of a w d Then,

and

Call the retum behre subtractiag the fmed lease 6ee the p s o rettun. Then, the

field-wi& poss retani, dmoted by II, is

Simihly, operatot 2's p s s rettun, denoted by a, is

Ptopomtion 4.1: Undet AbA3, the hIloaing results hold:

(a) both the ultimate tecovery of oil and the ~ggregate gr0811 set- of the conmon

pool de~egee nith the ntlmber of independent operatozs;

@) the value of a le- grmted tn an opezator decreases with the n w k of indepen-

dmt kaas in the common pool field.

The proof of Proposition 4.1 can be e d y obtained by diffe~e~tiating eqaation (4.12)

to (4.14).

Propasition 4.1 (a) dates two quate daims rqgarding the ultimate rea~vay and the aggregate rent tespectively. The ultimate na>- of oil dechhg with the namba of

opaatom caii be iaid to be an oil extraction phenornenon, mdting h m the underground

pressure depletion d y n d c s of oii pdudion. That a k g e n u m k of indepaiht o p

exators cruses lon economie rent, howeves, is the ratid outcome d a t e d wi th cornman

pioptxty p r o b h . Here, the number of operatom meamma the degee of production hg-

mentation. More operators represent a bwez degree of pduction mnantration, which

d t s in higher rent dissipation.

Proposition 4.1 (b) can be viewed as a comby of Proposition 4.1 (a). More operators

rihase a rbnnting fiddwide rent. The value per lease of course declines with the n d e r

of leaees in the field.

4.4 A Game Theoretic Mode1 of Strategic

a Cornmon Pool

Leasing in

In th% section, we maiyze land~wners' leasing behaviors. Conaider a simple environment,

where M landownexs each owns a fraction of the laad siirkee th& avers a homogeneous

common oil pool In anticipation of the cornpetitive behavior of lease operators, each

laadorner haa to decide how to grant production @ta to operators which spechbe in

oil prodiidion. If a landownez decides to produœ ail h h e & we tao dways view him u both the landowner and an operator, u if he signe a lease contract to hmireU OPt main

h m k how the kndownem toke advantage of the common pool by st~ategically c h m a

the produdion orgmhotion ( d t i p l e leasing). More spegdidly, ne modd laa~downers'

deciai01111 .e r game in which uch of them choom~ smiultaa~eously the nombet of leua he ot she d pant to independent operatom Fobwing convention, ne leder to l a a h e r s

and operators as lessorzs and lestma mspectively.

In order to rimplifg the analy& fiutha, the hbwing asmmption about luie anfracta

is made:

A4: The le- contract taJces the blbwhg Qrm:

1. Having paid a fixed ke to a h r , a le- gaina the fall production ri&t on a

pnipeded oil ttact aad retains the tight to the oil prodaad

2. Lesmm have aJI the bargainhg powa; that is, the luiiiy d f ir perkctiy am-

petitive. Th&, a lessot extracts dl the economic rent of oil production through

a b d Pae, .nd iessees make aaro profit.

3. Lewing is mstly. The muginal tramaction ait of aigning a le- h Q.

ksumption A4 attempta to captare the mitin chiuactexistics of a typical oil Iwe contraet. In order to make lemes aggxeseive in produdion, a kase cuntract nmdy

reqaires a l e s e to pay a large fbe up front aud gants the lessee up to 90 percent of the o l prodiiced. The assumption of a f h d k leore contract is an appmximation of antracts

of sach a type. We cao think of the contracthg pmœss of kashg as bllows. A hdowner

first proposes contracts in a tbit-or-leaveit f;rnh;n~ to many poteatid independent

opatatorr with simiiar opportMitg mds. The operators then d&de whether they WU

accept the contractil. The cornpetition wong thorre operators d .SE them with th& opportmity costs and luidowners with the enth rents. Finally, the leaaing ttansBCtion

cost is uummed to capture the cost and fictions &ded with leaae contracting.

Before solving fbr the eqnik'brium of the leasing game, we show kst, by the use of an

example, the potentid gains of the multiple leasing strategy to a lmdowner.

4.4.1 The Potenfial Gain of a Multiple Leaaing Strategy: An

Copsicler a commcm oil pool, where M = 5, U = Sl,OOO, Oûû, c = .OOl, and s = -5.

Among the five luidowners, we a a m e that ho1 ate str.tegically innocent, aiid one ia

strategidy eophiaticated. An innocent landoffila e i t k produœ~ oil harelf or gants

only one pmdndion b, wherear the sophisticated kndowner may grnt production

leases to multiple independent ope&as. Denote by 1 the nombet of indepepdent hases

the rophisticated 1.ndowner gante ; thos the totd n h of le- in tke comnon pool

1 + 4 Let f l and @ be the d t i n g profits of a typicai sophbticated and innocent

h à m n e ~ , mpctively. Ushg the e@'briam solution of the cornpetitive exfraction

game, ne obtaàn

and

and

where II is the total rent in the comm<w pool.

A simple Cadation generates the tobning table:

Table 4.2

Table 4.2 shows thd, aa the nomba of independent leaaes granted by the eophisticated

hdowner grors, the total rent in the conunon pool steadily decnuer. The eophiati~(~td

hdow~er's profit, howevex, inerer~ee iIritiaJly and then decxeaaes nith the nomba of

independent leases she grantir. When she has four lesses, het pmfit d e s 810,047,

whkh i s $3290 more thon the profit she makes if she gants ody one letue ekategy* Thur,

this example shows th&, &en th& other landownere gcant one lem eadi, the remaining

laridowner hm incentive to grmt d e r d y multiple leases. The qoestion, then, is will

l u i h e m chaotm to gant multiple h s if each of them is h e to do so?

4.4.2 Analyais of the Leasing Game

Eqpipped wïth the chuacterization of the eqaik'briam in the eampetitive exttaction game,

we non tnrn to aoalyzkg the equilibriam of the landowned leasing gaxne. U n k the

assumptions about leasing outliaed earlier, lesaors have dl the bugabhg power. Thus,

lessors arttact all the economic rent fiom le88ô8 t h u g h a k d l em h, leaving lsrreer to earn ztzo profita.

Let M denok the number of h r s in a cosunton pool, and 4 the namba of l e m

the leseor choosea to gant, whem m = 1,2, ..., M. Deaote the profit of lerror rn

by n,, which is her leasing revenue, nettiag the transaction cost of sigming these haseil.

Hence, we have

The example in d o n 4.4.1 shows that a Iandowner has an incentive to grant multiple

independent leases, if othas do not. We non taea to the symmetric Nash eqyilibrium of

the leasing game.

In the Nash ka&g game, a typid lessot m rn* r,,, by choohg Lm, taking as

&ai o t k le880ra9 number of leaaea. The fist oida condition fields

6Dr rn = 1,2, ..., M. Notiœ thab eqgation (4.16) is eynUrietnc br 9 mci, which impliea

the e ~ i r i o z p solution of L,,, is the same h r al1 m. Denote the e<roiiibriiua ncimbar of

haes of a typical lessor b 2. Then, we obtain

for M > 2, where w = 8 ie the dative muginal t r d o n cod of le-. Repiacing 1

by in the above equation yields

Eqtiation (4.17) determines the etpdibrium nomber of leases per hdowner. Eqaation

(4.18) charactezizea the relationship between the dqpee of prodaction cunomtration .ad

the degree of lapdownership conœntration.

Proposition 4.2: If the matginal transaction ad of leasing is dciently lon and M > 2, the subgame perfiect eqoilbrium hsii the hIlowing propaties: (a) eech landowner grante multiph hases; (b) the number of independemt leases inc~eases with the number of

hndowners in the field; and, (c) the n d e r of leases per landmer deaeases with the

namber of landowners in the field.

(Sse Appendix 4.1 tot the proof)

Proposition 4.2 (a) predicts kiidowners' multiple leasing behavios in a cornmon pool

with mote than two lmdownm. It a h implies that the degree of production oonœntr*

tion is bwer tham the degree of laiidownership aonaznttation. Proposition 4.2 (b) &.tu

that the degree of pmdnction conœntrathn M dete-ed by orid poaitively related to the

d q of landot~tlership conoentration. H m , more fragmemted landownership hada to

more âiapersed production control. PmpoPiüon 4.2 (c) hdicates that th- h a limit to

lan&wners9 strategic leaeiag. This is because the marginal transaction mat of leasing is

a mnstmt, but the total eamomic rent hm an uppst bound a d deciiaes ur the numba

of leases inamses.

In ordet to undentand the hzœs behind the landoftnems' leasing conaideration, we

remk the fuf order andition of the leuiiyl game u C>Iliows:

The doat tame on the LHS of the eqgation meumre huz Misent d e c t s of ganthg an

extra lerue on the prodit of 1e880r m: the ht tmn meaaures the gain in lessor m'r shw

of ultimate recovery, w i c h we &dl refer to as the & d a n c i n g de&; the second

tam mepcmrer the 108s of profit due to reduœd total m v e ~ y ~ which we d d t e k to aa

the &of-the-pie eflect ; the third term measures the pmfit loss due to incrreaeed drilliÿy

CO&, which we ehaU to as the oven9mstment &kt; aad the hurth tetm m e m

the ~ O S B due to the marginal transaction cost of leasing, which we ehdl refèr to aa the transaction &kt. The Iast t h e & d s are an negotire. Obviociiily, the shille-erihancing

&ecf of multilateral ieasing ia what induces s leaior to a a t e multiple leases. If a lesuor's

sh.n in totai output and nat wem k d under iome riiles, she wodd not grant multiple

leaeee.

Remuk: Multiple leasing strategy bendts a kmr, not because lessees have supezior

technologies, but becanse Cesami face diflérent extetllalities. Lessees of a mdti-lease lerror

ignore the extemality th& extraction U c t e not only on otha leslote, but dso on othet

lessees of the lessor. This malces lessees more aggersive in extraction than the leesor. By

grrathg production rights to multiple independent hasees, a lesmr aedibly mmmits to

a higha level of extraction and, congequenfly, iamease~ her ahare of the total output and

eoonomic rent . However, if ail lesgote pursue the ssme strategy, in eqnilibrium, everpone

is worse off. Neverthelem, &om an individual landowner'~ point of v h , multiple leasing

dwayi dominates grmting a single leocie. The outcorne of the l e d g game Y M a x to

that of the pkner ' r dilemma. Withont infiementione h m outsiders (the goveznment,

BDr example), iodividud rationaMy wdl debat the common i n t e .

4.6 Conclusion

This paper d e s leasing

that, despite the nnt dissipation d s t e d with nonconœnttoted oil extmwtion, it is

profitabk km a I.ndowner to gr& productioo *te to multiplie indepenbt fums. The key to this p d is the powa of CO rmnitmeDt in a mdti-stage noncoopezative game.

Thn,ugh multiple hdng, a hdolirner crediily mmmits to a higher &action rate and,

collsequently, captms a highe~ shin of output aiid rent. When the gah in ahare dom&

nates the loss due to the shtinting of fieldwide rent, it b rationai fbr a landowner to gant

an additional kuie to an independerit opaator. This aiialysis pmvides an a p - i o n

fat the puidhg ieasing behaviora of laodowners in U.S. onshore oil fields. OPt d t r

aLo indicate that inaightr h m thh phenornenon may have sigdicant implications br

the hrmation of efktive regulation policies.

Momover, the rtractud chuac tdcs that lead to kdowners' multiple le- strategb are also praient in many o k common properfy probhs. A mnceptually

s i m k p m b h is that of fishery in international waters. ki this case, each country wodd

have incentives to liame multiple finhing dirms to iaaease itcl l a r e in output. Li prin-

Qple, the kamewo~k of thb paper can be applied to .ny common property pmblem nith private acœsfi rights.

Chapter 5

Conclusion

Three essaye comprise this thesis. They study how iùms strategically set up autonomous

units when king cornpetition. ûur r ed t s iflustrate the importance of the hstitutbnai

arrangement and decisi0118 stmcture in a h, not ody to ite perhcfflma, but also to its

civais' p d t s d collstulllae' welfiue.

In the first essay, we show that a firm that produœs a goup of c o r n p h t e crrn

generate highez profits through divestittues, whea there is a cornpethg firm supplying

an impdct mbstitute groap of complaaaits. By dhgating pncing deaajons to inde-

pendent divisions, each 6rm aedi'bly oommits not to set the prices of the oomplapreiitii

within the group co~nsively, wEch softens the cornpetition. In 0 t h worde, by dividmg,

the hms cxeate negative extemalities among the prias within the groap that onset the

positive externaiity between the pricea amsa p u p s . The same idght also a p p k to

the case when firms sopplying impe&ctly mmplemmtary goods or d c e s compte by

setting qaantities. Onr analysis saggests that indudry stnictiire and siee of fitmil ue

detamined by the natnre of pmduds and the strategic considf?tations of the firmr.

The weüue implications of the divigionaljzation in o u model are dgdicant. Dive&

tues by the firmr mpp1ying complements taise prices and reduœ consumers' sll~plus.

Howmr, the profit gai^ axe not luge enough to compensate the consumerd Losses. As

a remlt, the total social muplus is redticed.

Anothez implication of out analgais is th& diveetitore motmted by pduct-line corn-

plementuity un be viewed as a respome tow.tde e n t ~ Suppose that, initiaûy, th- is

a mompoly that supplies a gocip of c o m p h t u g goodi ot services. Cledy, in oor

context, the monopoliet does not have any hcentim to divest itr operations. When po-

tential entzants enter the market and mpply dinezentiated products, the monopoiist h a two posaible responses. ûne ii to compete agajnst the entrants. If the entrants do not

make enough profits to cover th& en- eodil, the entries are detened. Il the pmductr

ofàaed by the entrants an dühentiated enough h m the incumbent's products, and if the entry cods are datively smaü, the entry unaot be deteme& bi this case, an o p

timal strategy br the incombent &m is to d e n cornpetition by divesting =me of its

opetaths. Oiu analyI suggeata that the optimcrl namba of divisions h r the incumbeat

in- as more enhaafs enter the m k t .

It should be noted h d y that onr malysia ie based upon a numbe~ of ammptions.

One crucial aastrmption is that divisions crslnot fartha divide before they choom thQI

prias. This is reasonable in certain situations wheze the pa,rent 6r-m~ rtül have mapt

ow~ership contxol of the divisions, but do not make management deBMns. Ekanrhinc?

contracts can be viewed as an example of mch a divhionalization. Li other situations, it

can be dia id t bt firmrr or divisions to mahe this type of cornmitment. Divisions may

thea hive incentives to divide futha. T b taises the issue of what determines a stable

industrg structure in the presence of both substitutes and complemeats. F M h a mearch

abng this liae is needed.

In the second essay, ne considet an environment in which cornpethg oligopolistic firmr

with Merentiated produds can set up independent rival divisions. We andp the strate-

Qc incentives for a 6inn to divihnalbe, chatacterk the eqpilibrinm of a divisiandhation

game, and highlight the effect of product dSerentiation in engtltmg asi interioz eqailib-

rim. By allowing bt prodiid diflkxentiation, we demonstrate that the existence of an

interior equilibrium un be ochiered without &œ on ad hoc assumptions such u an

exogenous bound of pamissi'ble nomber of divisions oc a costly divieionalbation.

We also coneider the conseQirences of allowing divisions to ftutha dinde. It is bund

that, if divisions are aUowed to fartha diiride, they a h y s w i L Then, the only possible

outeorne is the one in which the firm that aUows its divisiom to furthet M e haa infinite

numbet divigiona and zao profit. Hence, each fitm h a an incentive to anil.taaDy rertnct itr divisions h m fiutha breakup. Oor fiaiding pmvides a theoretical justification bt the

BgsOrnption in the gtr.tegc divisionaibation likrahue th& only parent fums can ret up

divieiona, and dbhbns cannot.

Findy, we disctlss the free d r y issue. We h d thai divieionalbation haa a naturd

entry deterrenœ property, fat it uii eignificamtly mogiig the Benntier of cornpetition

in the fkœ of aitry. As a r e d t , i n a m k t firme may perriitently e- abnormdy high profits in h e entry eqtiihiriam relative to the no divieion&ation In hret, when

Grmr have diflxculty to dkentiate h m each other becawe of either the concentration

of c o k e n r ' tastee or technological L~BOIUP, the only pote strategg nibgame pezkct kee

entry eqydibrium b the monopoly outcome, even if the en* amt L relatively lor. By

lllniting the niimber of independent diviaions or fianrhincui, regulatori can a c t d y help to

hcr- cornpetition. In addition, in contrast to the previo08 literatttte, which suggesti

that the incumbent actually has to set op divisions to deter entry, we show that the threat

to divisionpliae is enoagh to enme the monopoly ontcorne.

The third euay examines leasing behaviors of landownm in a comm<m oil pool We

show th&, despite the nnt disripaüon aasociated with nonocmceatrated oil extraction, it

i~ profitable ht a luidowner to gant production rights to multiple independent h.

The key to this p u d e is the power of cornmitment in a multi-stage noncoopaative game.

Throagh multiple leasing, a luidomet ctediiy commite to a hîgher extraction rate ~ n d , consequently, captures a highm &axe of output and r d . When the gain in shue domi-

natei the loss due to the k h k h g of fieldnide rent, it is rational Lot a landorner to pmt

a,n additional le- to aa independent operator. This analysie provides an eatplcuiation fat

the p d g Ieasing behaviots of hdowners in the U.S. onshose oil fields. Oiu d t s

.Iio indicate that inrights ftom thb phenornenon msy h a e rigiificant implications 6Dt

the Cormation of d ' i v e regulation policies.

Momver, the stmctu~al chatacte&itics that lead to laiido-' multiple leasing

strategies aze a b present in many 0th- ammon pmperty probleme. A amœptually

rimiLr pmblera is that of fishery in international waters. Li this ease, each country would

have incentives to liaense multiple fishing firmir to inc~ease its &are in output. In prin-

ciple, the fiamework of this papez can be appüed to any cornmon pm- p m b h with

ptivate acœsa righte.

NOTE TO USERS

Page($) not included in the original manuscript are unavailable from the author or university. The

manuscript was microfilmed as received.

This reproduction is the best copy available

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Pmof ofLemm<l~.l: The e t e n c e and u n i w e s s of the eqdibritm h b w fmm Etied-

man (1977). The symmetry of the equilibrium p h mthin the goap bIlowr h m the

necessary conditions (2.9). In whd hllows, we shaw th& the eqdibrinm aggregate

pticea, pi and pl, inaease with ml. Denoting 11 = (Pi,h) aad z2= &,fi) and applying

standard compuati-static techniques to (Il), ne obtah

Asaumptions (Al)-(A3) imply that A > O and 8fi/c?mt > O. And i?h/rPml > O hbws h m (A4). The prooh of statanents (d) and (e) are malogoas. Q.E.D.

Proof of Lemmu %!.a First notiœ thd, by Lemma 1, when mi = ml = m the eqnilibrium

aggregate ptiœ h r each group of the cornphente is synimetric, which we denote by

3m). Let 2 = Hm), 8m)). Then,

h m the brst-otder conditions (2.11), jj(rn) = -mD(z)/Dl(z). It CoIlows th&

(AS) hpliei that -D2@,p)/&@,p) is non-increasing with p, Lemma l(e) implies that

flm) increaaes strictly vith m, and (1 - m)/m stactiy h c ~ e a s e ~ with m. It ~ R O W B th& (1 - m)/m - D2(2)/4(2) strid.. demases with m and ie equal to zem at na = m*.

Thua, U(m, m)/dm is pomtive fot rn < m. and negative bDr m > m*. The clUm hIlows.

Q.E.D.

Pmof of Proposition Al: Let r% be the number of divisions in the symmetric equili'brium.

W e fùat show that > 1. Using (2.12) and (2.13), we obtah, hr oty ml,

Lemma 2.l(c) implies that 8j&/lhn1 > O. The daim b l b n s &om the hbwing inequality

Nat, we show that h < mm. Suppose to the oontry that Ga 2 m.. By Lemna 2.1,

when ml = ml = na the eqaik'btipm -.te pnœ ht each gbop ~f the complements is

symmetnc, whieh we denote by $(na). Let z = Hm), flh)). It h h w a h m (2.12) and

(2.13) that, at ml = ma = fi,

is the derivative of the eqnilibrium groap priœ & with respect to mi

= m a = h , k = 1,2.

By the defmition of me, @(naL) = p~ and the hIloWmg eqaafion

holda at m = mm. The left-haad aide of the above eption stnctly bcrieasea with m,

(AS) implies th& -Da@,p)/Rl@,p) is non-incfeasmg in p, and Lemma 2.l(e) impliea

th& Hm) in~eases with

in- in m. Th-,

m. It QJlows that -D2(P(rn), Km))/&@(m),P(m)) h non-

wheze the la& inequality h b w s b m (Al) and (A3). This conttadicfr with the neœssary

condition fat f i a to be the ~ymmetnc N d e+irium n u b e r of divisions. Tb daim

hlbwi, Q.E.D.

5.2 Appendix 2.B: An Integer Divisionahat ion Game

Li this appendix we andyze an in* game in which the numbezs of dîvisiona, mi

and ma, choren by the fimm an d c t e d to ba integerr. The questio~ aie whethez

it is d possible hr the fi- to orhieve the monop01y p d t r by c 0 0 r U g t W

divisionalization stratefies and whethet there exista a pure drateay Naah eqoilbnum in

the non-mgmative divieion gsme.

For simplicity, we consider ody the lin- daiwd fundion (2.2). The red~ce~hrm

psyoff fanctions are represented in (2.16). Let rn* and th be the opthdly coordiarted

number of divisions and Nash eqnilibrinm number of divisBo- in the mntinuotu division

game discussed in Secfion 2.3, respectively. We aqpe that br large ni aad na the fivrmr

may not in genad be able to replicate the maximum pmt profit by coordinathg th&

division stmtegies, but can almost achieve the maximum pint profit. The optimally

coordinated namber of divisionri in the integer game is dose to mg. Moreover, there

dways &B a pare sttategy Naah eqdibrium in the integer game and the eqailibrium

anniber is close to 6.

Let [ml be the integer part of a rerl number rn, i.e., the infeger such th& m - 1 < [ml 5 m. Consider firat the non-cooperative division game. Denote [fi] by I . Sinœ the

payofl fot f i 1, V(mi, ml), is a siiyle-pealtrd function of mi, the best-nply of h 1

to an integer ma is eitha [R(m2)] or [R(rn2)] + 1. Uoreover, since R(m) ie monotonically

increaaing and sbpa of R(m) are akways kse than 1, the best-reply to I is either [R(h)] ot [&(fi)] + 1. Similady, the bebreply to 1 + 1 is either [R(k + l)] or [R(& + l)] + 1. It

h h w s that (1 , I ) is an eq@binm if

It neither ineqpality holds, then both (1, I+1) and (1+1, I ) ue Nash ecpdibria. ThabDn, there exists at lead one pon skategmy Nash eqriih'bniira th& is cloae to the eqoilbritun

Table 5.1: The Papff Matrices in the Divirion Game

in the continuou8 dbihn game.

The coordinated divisionalizakion works in a shdiu way. The joint profit is V(m1, ml)+

V(m2, ml), denoted by P(rni, ma), which is ~ymmetnc in mi and ml. It cro be e d y

shown that, for any ma, P(ml,m2) h singbpeaked in ml. Suppoae th& the peak of

P(ml, ma) is reached at mi = R(m2) (i.e., the best reply fandion). k l y , m* = R(mm) . It can be verified that the dopes of R(rnl) is between O and -1.' The -le-peakeànees

of P(ml,m2) implier th& for an^ ma the m-tlpa is teached eithex at [R(m2)] or at

[R(m2)] + 1. Since the sbpe of R(m2) is between O and -1, the epmmdry then implies

that the maximum of P(mi, ml) is reached at one of the tollowhg pairs: ([me], [ma]),

([m.], [m) + 11, ([m.] + 1, [mm]), or ([m*] + 1 , [ 4 + 1). In the hIlowing, ne provide an example in which a = 10, /3 = 6 , ~ = 4, and nl =

n? = 4. Notiœ th& m* = 3 and rî, = 1.34. The pôyoiE matrices in the integer division game u e repregepted in Table 1. The joint profita are r n m r h k i at ml = ma = 3. There

ate two pure strategy eqailibria, (mi, na2) = (1,l) and (ml, ml) = (2,2).

Figura 2.1: The Beet-Reply Lines in the Priœ Game (the Linear Demand Fbctiom)

S.3 Appendix 3

Pmof of Lemma 3.1: The eWtenœ U triviaRy rhorn b m equation (3.6).

(a) Divide equation (3.6) by and rcMnge it to obtain the output of a division in firm

and

(a) DBerentiate eqgation (3.6) with mpect to mr, and to get

and

P m f of Proposition 8.1: Lemma 3.2 shows that nnmbas of diviaions an atrategic

complementr. Thus, the first stage solution mast be symmetric- If not, without bar of

generdty, denote ml 5 na2 ... m., the solut ion, whae at lead one of the ineqaalities

holb sfsictly. Then, mi < m,,. By the ggmmetq of the tùst orda condition, any ordering

of U a solution. In partictrlat, consider the o r d w m,,,m2,m~, ..., m,+l,rn~. Iii the

new ordering, the nomba of dipieions of fum 1 incmms h m ml to na,, and th& of

km 2 to firm n - 1 stays the iame. By Lemxna 3.2, the numbez of divisiana of fum n

ahodd i n m . However, it demmes h m m, to ml. It ir a co~ltradi&*on. T h d r e ,

the solution Gr the fita stage gaine is symmeLEc. The miquenesa is directly implied by

equation (3.10).

To show the comparative atatic redts, dehe G(m, z, n) = m2(l - z)((n - 1)z + 1) - m(n - 2)r - 1 = O. Th-,

R e d fiom section 3.2 th& m < A. Thus, # < O and < O fot n 2 2. Then,

and

Q.E.D.

P roof of Pmposition 3 3 Remange eqnation (3.11) as the hllowing:

a2 = E i

[b& + (1 + z(" - l))a=

First, totdy dift'tiate the above eqaation wr.t. n and z to get

Then, $ < O. SHddy, tete ddkentiate eqafion (3.11) w3.t. n and F to get

Q.E.D.

Pmof of Pmpoeition 3.4: At n = 2, rn = Js (hm equatiom (3.10)) and the p d t

Then, the doopoliirt's profit is no greatex than F if z 5 z*. Q.E.D.

5.4 Appendix 4.1

S.O.C. of the leasing gune:

Differentiate F W. r. t. its illgammts:

@) g = - ) r . < o , b r ~ > 2 ;

(c) & = 0% >O, br M > 2;

(d) = -& <O, br M > 2.

(c) and (d) validate (a) and (c) of Proposition 4 3 ~ c f i v e l y C

5.5 Appendix 4.2

Table 4.1: Leases and Operators Distribution by Fields

l a 18 e

'II 0

10 14 17 6 7

16 I O 1s 12

O 61 2s a 14 10 20 18 7 4

41 16 41 26 28 IO 1s 1s a a 1 II 16

101 m 42 sa 32

0.6 @.O 20 3.7 &O 6.3 4.7 4d 4.6 1.8 4.0 2.6 aa 2.4 13 6d4 m u ia 4A 22 14 Od u 4.1 1.6 9.4 2.1 1.9 0.8 1110 1.0 1.4 : 12 0 4 0.7 S.? aa 12 f.6 O.?