ganesh iyer* & david soberman**
TRANSCRIPT
CONTRACTING FOR "RETENTION" AND"CONQUEST" FACILITATING INFORMATION
by
G. IYER*and
D. SOBERMAN**
98/40/MKT
Assistant Professor at the John M. Olin School of Business at Washington University in St. Louis.
** Assistant Professor of Marketing at INSEAD, Boulevard de Constance, 77305 Fontainebleau Cedex,France.
A working paper in the INSEAD Working Paper Series is intended as a means whereby a faculty researcher'sthoughts and findings may be communicated to interested readers. The paper should be considered preliminaryin nature and may require revision.
Printed at INSEAD, Fontainebleau, France.
Contracting for "Retention" and "Conquest"Facilitating Information
Ganesh Iyer* & David Soberman**
May 1998
* Ganesh Iyer is an Assistant Professor at the John M. Olin School of Business at WashingtonUniversity in St. Louis** David A. Soberman is an Assistant Professor at INSEAD in Fontainebleau.
e-mail: [email protected] and [email protected]
Contracting for "Retention" and "Conquest" FacilitatingInformation
Abstract
An important use of information in today's information-intensive businessworld is to facilitate the modification of existing products (a recent survey concludes
that 80% of new product activity involves modifications to existing products). In fact,
information and expertise, which helps identify consumers' preferences for differentattributes, is critical to the development of a profitable product modification strategy.
Many independent vendors possess such information and a key question for a vendoris how to contract the use of this information to downstream firms.
The paper focuses on two distinct types of product modification information.
The first type of information allows a firm to implement modifications that increase
the attractiveness of the product to the firm's loyal customers. We label this as"retention facilitating information. In contrast, a second type of information,
labelled "conquest" facilitating information, allows a firm to implementmodifications that increase its appeal to competitive customers.
We examine two important aspects of the vendor's contracting problem. First,
we consider whether or not a vendor has an incentive to contract such information to
a downstream firm on an exclusive basis. Second, we look at a broader question of
which type of information (i.e., retention or conquest facilitating), an informationvendor would like to sell if she indeed had the ability to sell either. For instance, weidentify the conditions under which the vendor would prefer to suppress the sale ofconquest facilitating information while promoting the sale of retention facilitating
information.
We address these issues by developing a game-theoretic model consisting of
an information vendor who faces two downstream firms who sell differentiated
products. The model analyses how contracting for information is affected by the
degree of differentiation in the downstream market and the power of the informationin terms of the impact of the resulting modification. We find that the optimalcontracting strategy for retention facilitating information is to sell non-exclusively toboth competitors. Conquest facilitating information, however, might be sold under an
exclusive contract. Intuitively, retention facilitating information effectively increases
differentiation in the market leading to an increase in the market prices. The effect of
conquest facilitating information critically depends upon how powerful the
information is. Less powerful conquest facilitating information makes marketsbehave as if there was very little product differentiation. In such a case, trade in
conquest facilitating information is not possible because it significantly reducesmarket prices. However, once the power of conquest facilitating information is above
a certain threshold, a vendor will find it optimal to contract such information
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exclusively to a downstream firm. Interestingly, we also find that when conquestfacilitating information has extremely high impact, a vendor is indifferent between
exclusive and the non-exclusive contracting strategies.Finally, when a vendor is able to choose the type of information she sells, the
optimal type depends on the power of the information and the extent of differentiationin the market. With less powerful information and in markets with high
differentiation, the vendor prefers to sell "retention facilitating" information.
However with information that is powerful and in markets with lower differentiation,
selling conquest facilitating information yields greater profit.
Key Words: marketing of information, exclusive contracts, "conquestfacilitating", "retention facilitating", product modification.
1. Introduction
A recent survey concludes that a majority of new product activity involves notcompletely new products, but modifications to existing products in the form of line
extensions or changes in product features 1 . As Kotler and Armstrong (1996) mention,
in mature markets where competition for market share is high, modifying the productto changing consumer needs and market conditions is a frequently used strategy. Acritical ingredient for developing a successful product modification strategy isaccurate information about consumer preferences for different product attributes.Market research information lies behind many well-known product modifications
such as the revitalisation of Aqua Velva® aftershave or the decision of Mobil to
change to a "Friendly Service" format with an emphasis on attendant pumping and
station services2 . Despite the obvious importance of product strategy in the overallmarketing mix, there exists no study in the emerging literature on information-intensive marketing that examines markets for information that aid product design and
modification.Many markets have seen the emergence of a new source of information that
aids product modifications: organisations that collect information as a by-product of
their primary activity. These include organisations such as magazine publishers,
tourist authorities, airports, sports organisations and government bodies. In the past,
organisations archived such information and never thought of it as a valuableresource. However, with the advances in information and computer processing
technology and the importance of information intensive marketing (Blattberg Glazerand Little 1994), the managers of these organisations find themselves sitting on a
Gorman's New Product News reported that 89% of the 6125 new products accepted by grocery storesin the first five months of 1991 were line extensions.2 Many such product design changes are discussed by Wansink (1997). The Mobil example isdiscussed in the Wall Street Journal, January 30, 1995. Mobil followed up on research information tochange its product offering and went upscale at the pump, with cappuccino in the convenience store, aconcierge to assist customers, and what may be the cleanest gas-station bathrooms ever.
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valuable resource. For example, airport authorities at most major internationalairports regularly collect the nationality/airline/address and travel habits of passengersarriving at the airport. This information is valuable to both airline carriers (indesigning their airport and on-flight services) and to hotels and restaurants. Thuswhile in the past the traditional source for product modification information has beenindependent commissioned studies conducted through market research firms, there isnow greater availability of information from outside vendors who collect it as a by-product. Our study addresses this trend towards the selling of "information by-products" by many organisations. Table 1 presents some facts on the different typesof organisations that sell information by-products3.
Table 1
Type of Nature of the Information by-product Potential BuyersOrganisation availableMutual Funds and Client trades, investment level, income, Financial Publications,Brokerage Firms age, marital status, homeownership, family insurance agencies, mail-order
size and characteristics companies
Retail Chains and Purchase profile, spending, and Manufacturers of consumerDepartment Stores information about age estimated income,
type of home and other data fromapplication from store credit cards
products, market research firms,financial institutions,.
Credit Bureaus Balances on credit cards, payment history,mortgages, loans, family information
Lending agencies, employers,direct marketers, utilities
Airlines Travel habits, personal data of frequent
fliers, use of ancillary services such asRental car agencies, hotels,
credit card issuers, travelhotels, rental cars , flight scheduling
informationagencies
Government Property holdings, tax assessment, land Consumer product firms, realrecords, census information, postal data,
traffic dataestate companies, utilities,mapping services, service
providersPrivate vendors (e.g., Mortgage data (Lusk), household mailing Manufacturers of consumerThe Lusk Company, lists (Polk) productsR.L., Polk, DonnellyMarketing )
Source: Records Management Quarterly (1996)
Brand managers typically can use information to implement two distinct typesof product modifications. The first type is a modification that increases the appeal of
a product/service to loyal customers of the product. As an example, Red Lobster®
converted the exteriors and interiors of its restaurants to a "wharfside" look because
3 "Selling Information: What Records Managers Should Know," Records Management Quarterly, 1/96
3
market research information indicated that existing Red Lobster customers wantedexperiences that took them away from the grind of everyday routines 4. We label this
type of information as "retention facilitating information." In contrast, the secondtype of modification is one which increases the appeal of a product to customers ofcompeting firms. An example of this is the use of information by Ford to engineer theradical new styling of Ford's small cars in Europe that started with the launch of the
Ford Ka® in 1996. The new styling was more attractive to non-Ford buyers than to
loyal Ford customers. We use the terminology in Colombo and Morrison (1989) andlabel this type of information as "conquest facilitating information." We examinehow contracting for information is affected by the type of product modification that it
facilitates.We analyse the optimal contracting for the different types of product
modification information as well as how such information affects competitionbetween firms in an industry. The paper examines the manner in which the optimalselling price is determined for such information and whether it should be soldexclusively or broadly to competitors in a downstream market. We also examine thebroader question of what type of information would the information vendor choose to
sell, if it indeed had the ability to choose. In other words, if the vendor had a choice,would he prefer to sell retention facilitating or conquest facilitating information and
how is this choice governed by market conditions?To examine these issues, we develop a model of an information vendor selling
to two differentiated downstream firms. Differentiation between the firms is capturedby a spatial model with two firms located at either end of a uniform linear market.The vendor first decides on the selling contract. Given the contract offered by thevendor, the firms make decisions on whether or not to buy the information. Finally
the firms compete by simultaneously choosing market prices.The paper traces the impact of information on downstream competition
between the downstream firms and the optimal contracting strategies of the vendor to
two basic factors: the degree of differentiation and the "power" of the information in
terms of how valuable the resulting product modification is. We find that theequilibrium contracting strategy for retention facilitating information is to sell the
information non-exclusively to both competitors. This is because retentionfacilitating information unambiguously increases the differentiation in the market.This reduces competition and as a consequence, market prices increase. For thevendor, a non-exclusive strategy is superior because it helps the vendor to extract
more surplus from the downstream market.The effect of conquest facilitating information on competition between the
buyer firms depends critically dependent on how powerful the information is relative
to the existing differentiation between firms. When the information is relatively lesspowerful and the extent of differentiation between the firms is strong, conquest
4 From "Magic Make-overs", Restaurant Hospitality, November 1997, p.50.
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facilitating information is unlikely to induce the loyal consumers of a competing firmsto switch. Nevertheless, each firm still responds to the other firm's increased abilityto attract its loyal consumers and prices aggressively. Thus conquest facilitatinginformation of the "no switch" variety increases price competition and makes marketsbehave as if there is lower product differentiation. In such cases, the sale of conquestfacilitating information is not possible because it reduces market prices. In otherwords, the information market unravels. However, when conquest facilitatinginformation is sufficiently powerful relative to the differentiation in the market it cansold under an exclusive selling strategy. In this case conquest facilitating informationhas the ability to "switch" the competing firm's loyal consumers. Moreover the
exclusive possession of conquest facilitating information can help a firm to drive theother firm out of the market. Therefore, a downstream firm will pay a high price forexclusive use of the information. We also establish an interesting result for theextreme case of markets with very strong conquest facilitating information relative tothe differentiation between the firms. Here a vendor becomes indifferent between theexclusive and the non-exclusive contracting strategy. In these markets, the ability ofthe exclusive buyer to take advantage of the information and charge a higher market
price is tempered by the fact that this high price might result in loss of its loyalcustomers (who are less affected by the conquesting modification).
Finally, when a vendor is able to choose between selling retention or conquest
facilitating information, we fmd that the sale of retention facilitating information willbe more prevalent when the information vendor's product is less powerful relative tothe level of differentiation. In contrast, the motivation to sell conquest facilitating
should be strong when the impact of the information is high relative to the level ofdifferentiation.
The paper will proceed as follows. The following section providesbackground to the problem in question and relates the analysis to existing literature.The model is presented in section 3.0 and the solution and results are presented in
section 4.0. In Section 5.0, we discuss the implications and conclusions of the study.
2. Related Research
The primary focus of this paper is the selling of information that facilitatesdifferent types of product modification. Prior to discussing the nuances of selling
information, it is important to recognize that a large body of research in marketingexamines strategies for modifying products and their attributes. An importantmethodology in this area is conjoint analysis (see Green and Srinivasan, 1990 andGreen and Kreiger, 1989 for reviews of this literature) which measures consumerpreferences for products as bundles of attributes. A primary use of conjoint analysisis to measure the value of product modifications and assess their likely impact prior toimplementation. Another approach pioneered by Hauser and Shugan (1983) uses amodel in multi-attribute space to analyse the modification (or repositioning) of a
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product in a market with several competitors5 . In spite of marketers' interest inproduct modification strategies, there are no studies which consider the problem of avendor who wishes to sell information that can be used to facilitate productmodifications in a competitive market.
Because of our paper's focus on the selling of information, a review of theexisting literature on information as a product is necessary. First, it has manyelements typical of a public good and second it is primarily an intermediate good (itderives value from what it allows an individual or a firm to do). Our frameworkcaptures both of these properties. Consider the first property: the public goods natureof information. An essential property of a public good is that its consumption by oneindividual does not prevent others from consuming it (Samuelson 1947; 1954). Thisdescribes the situation of passenger data possessed by an airport authority or customerinformation gathered by a research firm. Once information is in a form that is useableby firms, the seller incurs close to zero costs to provide the information to an
additional firm. This aspect is accounted for in the model, in that the information
vendor can sell to both firms (non-exclusive) without incurring additional costs over
the choice of selling to only one of the downstream firm (exclusive). However,
information does not fully meet the definition of a public good because it does notpossess the second essential property of a public good: that its consumption by onedoes not reduce the enjoyment of others who are already consuming it 6. This isbecause in a competitive industry, the possession of a bundle of information by onefirm can diminish its value to a second. This is due to the intermediate nature of theinformation and the fact that its value is determined through the competitive
interaction of the downstream firms. Our model captures this characteristic of
information by modeling the competitive externalities between the downstream firms
and by showing that a vendor might not treat even homogeneous downstream firmssymmetrically (see also Admati and Pfleiderer, 1986).
Several authors have examined the selling of information in contexts differentfrom the one presented in this paper. Chang and Lee (1994) consider an optimal
pricing problem for a marketing consultant selling market research to manufacturers.However, Chang and Lee do not consider differentiated markets and the products intheir setting are homogeneous. Sarvary and Parker (1997) address a differentsituation of two upstream consultants selling noisy information to risk averse firmsand show that the externalities between the products of different consultants can leadto situations in which a consultant can be better off facing competition than if he were
a monopolist. Soberman (1997) considers the problem of an information seller who
has information that can improve the effectiveness of informational advertising.
5 A complete review of product design models is provided in Lilien, Kotler and Moorthy (1992).6 For example, the benefit of a lighthouse (the standard example of a pure public good) to a passingship is independent of how many other ships use the lighthouse for navigation.
6
Firm 1Decision
FkmDecision
Figure 1
Extensive Form of Stage 1
The Selling of Information to Competitive Firms
InformationVendor
pricingdecision irdormotion Vendor
P.
1;'x,P,
wi
2P.
Legend
Fkm profit with Information when competitor does not
Firm profit wehcirt Information when competitor has It
Arm poets when neither hove infccmcMon x.
Arm Profits when both hove bformalion f‘b
Non-exclusive Pdce (chosen by information vendor)
Booluslve Price for Finn 1 P,,
ExclusWe Price for Fkm 2 P.
Inform:Mon Vendor pricingdecision
Fkm 2Decision
Fkm 2Decision
0. P.
3. The Model
The model we develop has two stages and three types of players: consumers ina product-market, two competing firms, and an information vendor. The first stage isthe pricing and selling of information to competitive firms by an information vendor.The information vendor chooses between selling to one firm exclusively or selling toboth. The second stage occurs after the competitive firms have decided whether ornot to purchase the information. It consists of the firms simultaneously setting pricesfor their product. Then, consumers decide which firm to buy from based on theirpreferences and the observed prices of the firms.
The Vendor of Information and Stage 1
The information vendor's objective is to maximize profit from the sale of the
information by choosing to contract the information exclusively or not. The vendor is
forward looking and anticipates the optimal prices for each possible contract strategy
and then uses these anticipations to compare the returns from each option. Theextensive form of this stage is shown in Figure 1.
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The key decisions made by the players in Figure 1 can be summarized as
follows:
Step 1. The information vendor chooses selling approach (exclusive or not).
Step 2. The information vendor sets prices for information conditional on the selling
approach that he has chosen.
Step 3. Firms make decisions on whether or not to purchase the informationconditional on the terms and price offered by the information vendor.
When the information vendor chooses an exclusive strategy, he cannot sell the
information to the second firm if the first firm accepts the exclusive contract. In
general, exclusive contracts are legally binding and have sanctity in a court of law. In
the U.S., exclusive contracts are subject to the rule of reason and in Canada the onlyanti-trust challenge to an exclusive contract is that it constitute an "abuse of dominant
position"8 . However, it is important to note that once an exclusive offer is rejected,the vendor has the option of offering the information to the second firm. In Figure 1,
Firm 1 receives the exclusive offer first but because the firms are symmetric prior tothe sale of the information, this is arbitrary. Note that under the exclusive strategy the
information vendor's pricing strategy consists of a price offer of l'x i to the first firm
and a price offer 13x2 to firm 2 if the first firm rejected the vendor's offer. Finally, note
that under the non-exclusive strategy, the offer is made simultaneously to both firms.In Figure 1, the three dimensional outcome vectors describe the payoffs for the
information vendor, Firm 1 and Firm 2 for each decision combination. These payoffsare determined based on competition in the product/service market given thedistribution of product modification information implied by the branch of the game
tree. The profits (9ra , ltd) describe the equilibrium profit for firms in the fmal part of
the game when one of the firms has the information to implement product
modifications and the other does not. The term, Kb is the equilibrium profit for both
firms when they have the information and make product modifications. The term, 7r,
is the equilibrium profit for each firm when both firms do not implement any product
modifications.
•Strictly speaking, under the exclusive approach, the information seller sets the price for a secondservice provider after the service provider rejects the offer (there is no reason why the informationseller should be forced to set a price for the second provider before the first provider makes herdecision). Analytically however, there is no difference between this structure and one in which theinformation seller chooses both prices prior to the first service provider's decision.8 See Continental TV Inc. v. GTE Sylvania Inc., U.S. 36 (1977) and Preston (1994) and the Director ofInvestigation and Research v. NutraSweet (1990), 32 C.P.R. (3d) 1 regarding the legality andenforceability of exclusivity contracts.
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The second stage of the game (which occurs after the information-sellingphase) involves decisions by firms and customers. First, let us consider the product-market competition between the firms.
Stage 2: The Competitive Market
The market consists of two identical firms who offer competing products. Theprofit functions for the two firms net of any payments for information are:
= (p1 – c)x, (1)
= (p2 – c)x2 (2)
where pi and p2 are the prices chosen by each firm, and xi and x2 is the demand foreach firm's product and c is the marginal cost for each unit of the product servicedelivered. Given the Stage 1 contracting for product modification, each firmsimultaneously chooses its market price to maximize profits.
The products of the firms are assumed to differ with respect to an attribute andthe market is made up of customers that are uniformly distributed, with unit density
along an attribute of unit length (i.e. the total number of consumers in the category is
normalised to one unit). A product located in the same location as a consumercorresponds to that consumer's ideal service and the two firms are located at eitherends of the market. Thus, the consumer's location on the line represents thatconsumer's relative preference for the two competing products. We assume that each
consumer purchases at most one unit (if at all). For each consumer, the surplus that aproduct provides is a function of the consumer's preference for product that dependsupon the consumers' location on the line, the attributes of the product and the price atwhich the product is offered. Let us first consider the consumer's surplus for an
unmodified product. For a consumer located at x (the distance from the left endpoint),
the following quasi-linear surplus function represents the surplus delivered by the
unmodified product of Firm 1 and 2 respectively:
CS, = R– p, – xt (3)CS2 = R – p2 – (1 – x)t (4)
where t represents the psychological preference cost (or the travel cost) of theconsumer for not consuming her ideal product and R is the reservation value for theunmodified product. Next, suppose that the firms have the information and therefore
the ability to modify the product. In this case the surplus functions will be:
CS, = R + vi (x)– p, – xt (4)
CS2 =R+v2 (x)– p2 – (1– x)t (5)The function v,(x) represents the incremental benefit that a consumer at x will get
from consuming firm i's modified product. Note that this incremental benefit is afunction of the consumer's location or relative preference for the two products. Thus
if vi(x) is decreasing in x, then the information facilitates a product modification inwhich the firm's loyal consumers get a greater incremental benefit than the consumers
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Figure 2
The Effect of Retention Facilitating Information
available surplusbefore travel costs
13
The Effect of a Modificationbased on Retention Facilitating
Information for Firmi
Reservation Value 'R'for Unmodified Product
Firm 1 1 1 I Firm 2Linear Market of Unit Length
who are less loyal. This is therefore a characterization of "retention" facilitatinginformation. In contrast, if vi(x) is increasing in x, then the information facilitates aproduct modification in which the firm's loyal consumers get less incremental benefitthan the consumers who are loyal to the competing firm's product. This represents"conquest" facilitating product modification information. For the analysis, we will
use the linear functional form vi (x) = /3(1 x); v2(x) = fix to represent the effect ofretention facilitating information for firms 1 and 2 respectively. Figure 2 shows theconsumer surplus functions for this case.
Note that in this formulation )6 is the "power" of the information in terms of how
valuable the resulting product modification is. A greater implies that the product
modification is more valuable to all the consumers in the market. Along the same
vein, vi (x) = fix; v2(x) = P(1—x) represent conquest facilitating information for the twofirms. Figure 3 below shows the consumer surplus functions for conquest facilitatinginformation.
Figure 3
The Effect of Conquest Facilitating Information
available surplusbefore travel costs
The Effect of a Modificationbased on Conquest Facilitating
Information for Firml
Reservation Value 'Frfor Unmodified Product
Firm 1 i I Firm 2Linear Market of Unit Length
9 The term "conquesting" is borrowed from Colombo and Morrison (1989) who use it in the context of
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The surplus function v1(x) is in the form of a sloped line and it represents whatinformation does in this framework. It is therefore, important to understand theprecise meaning of the sloped line in terms of representing the power or the impact ofinformation. The locational differentiation between the consumers on the line or thepositive preference cost t represents a primary attribute of differentiation between thetwo firms. For example, if the primary attribute of differentiation betweenBreathSaversTM and CloretsTM breathmints were the strength of the taste, withBreathSavers having stronger taste and Clorets having a milder taste, we couldrepresent the breathmint market as a straight line with BreathSavers at one end andClorets at the other. Now the sloped function v,(x) can be thought of as information onhow to modify another product attribute which is highly correlated with the primaryattribute of differentiation. This correlation could be such that the modifications aredifferentially attractive to different consumers along the line. Going back to ourexample, suppose the manager of . BreathSavers obtains research indicating that
positive feelings towards chlorophyll, (a breathmint ingredient) are highly correlated
with preference for Clorets. The BreathSavers manager could now modify
BreathSavers to include chlorophyll: this is a prototypical conquest facilitatingmodification as it would increase the appeal of BreathSavers to Clorets users whilehaving relatively little effect on the preferences of current consumers ofBreathS avers 1 °.
In this framework, we describe the demand faced by firms 1 and 2, givenprices, as x and (1-x) respectively, where the x is determined by the incentivecompatibility constraint or the point where CSI = CS2. This assumption implies thatthe consumer at x (the marginal consumer) gets equal surplus regardless of whethershe buys from Firm 1 or Firm 211.
We will end this section by presenting the base case of a market in which no
information is used by both firms. This means that the two firms compete with their
unmodified products that deliver consumer surplus as in (3) and (4). It can be verified
that the equilibrium is a symmetric equilibrium. The equilibrium prices will be given
by pin = P2n = c+t and the equilibrium profits are gin lt2n = t/2. This base case cannow be used as a benchmark to compare the effect of modification facilitatinginformation on the product market equilibria.
We will now examine the optimal contracting strategies of the informationvendor. For each type of information we will also examine how the information
affects competition between firms in the product market sub-game. This will then
help us to better understand the forces governing the contracting strategy that is
finally chosen by the vendor.
a brand switching model applied to the automobile market.to This example is based on a product modification made to BreathSavers in Canada in 1986.II We restrict our attention to markets in which all consumers buy given competitive pricing. This isanalogous to assuming that R> t+c.
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4. Contracting Strategies for the Information Vendor
The basic aim of the paper is to identify the optimal contracting strategy for avendor who sells information that facilitates product modifications. Our analysis willproceed in two steps. We will first investigate how broadly the information should besold. In particular, we will investigate whether the vendor should sell the informationnon-exclusively to both the firms or restrict the sale to a single firm and how dependson the market conditions and upon whether the information is of the retention orconquesting variety. The second step in our analysis will be to examine the questionwhich type of information the vendor should sell if she indeed has the choice to do so.
4.1 Solving the Information Vendor's Game
We begin by discussing how the equilibrium profits of the information vendorare determined. To determine the profits of the information vendor, we need to
determine the price of the information under an exclusive contract and the price of theinformation when both firms buy under a non-exclusive contract (denoted by Px1 andPb respectively in Figure 1). There are two exogenous parameters of importance:
1. The transportation cost (t) which indicates the level of differentiation between
service providers.
2. The "power" of the information fi
Determination of Px1 and Pb
Under an exclusive strategy, the information vendor sets two prices as shownin Figure 1 because it allows him to extract maximum surplus from the firm who
receives the offer first. The information vendor sets Px2 low enough so that the
second firm buys the information. The first firm knows that the information seller
will sell the information to the second firm (this is a credible threat) implying that she
will make a profit of 7rd in the subsequent price competition sub-game if it does not
buy the information. This profit 7rd therefore represents the equilibrium profits of the
firm which does not have then information when the other firm has the benefit of the
information. In contrast, if the first firm accepts the information vendor's exclusive
offer she will make Ka in the pricing sub-game. The profit Ka therefore represents theequilibrium profit that the firm will make if it had the information while its competitordid not. Thus, the first firm will pay any price for exclusive use of the information up
to Za - ?td.
Consider now the non-exclusive strategy for the information vendor. Note
that the profit from selling the information non-exclusively requires that both firms
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buy. Using Figure 1, the following inequalities must be satisfied to ensure that bothfirms buy
7C a — Pb "-� 7C n A 7C b — Pb � 7C d (6)
Pb � n a –7c. A Pb � n b – nd
(7)Rewriting this:
Pb � min(n, – n n , 7t b — n 3
(8)
Both terms in (8) must be calculated for each and every set of exogenous parameters
that is analysed. The information vendor will therefore choose the non-exclusivestrategy depending upon whether 2Pb or Pxi is larger. With this discussion in place,we are now ready to examine the optimal strategies for the different types of productmodification information.
4.2 Retention Facilitating Information
Consider the case of retention facilitating information. We begin by solvingthe product market sub-game. Since, it is possible that the information vendor might
choose an exclusive or non-exclusive contract (and also that each downstream firmmakes a decision whether or not to buy the information), there are 2 different types ofproduct market equilibria that are possible for each type of information in addition tothe previously discussed base case:
a) an equilibrium in which both firms have the information andb) an equilibrium in which only one of the firms has the information.
We will impose the following notations for the rest of the paper. The
equilibrium prices and profits when both firms have the information will be denoted
by the subscript V. When only one of the firms has the information, then the prices
and profits of that firm will be denoted by the subscript 'a' while those of the firmwithout the information will be denoted by 'd'. When neither firm has theinformation, the price and profits of both firms will be denoted with an 'n'. Inaddition the case of retention facilitating information is denoted by the subscript `e.
Equilibrium when both parties have the information
When both the parties have information which helps them to make retention
facilitating product modifications, then the demand functions of the two firms inequilibrium is given by the (incentive compatibility) condition,
13(1– x)– p1 – tx = fix – p2 – t(1 – x) (9)
13
(12)n 2
(t + -:-)gar 13 +2t
t + 12
3 )6 +2t
fl + t – p l + p2 This yields Firm 1's demand function as xibr = x – , while firm 2's
2(/3 + t)
demand function will be x2br = (1-x). Substituting this for x 1 and x2 in the profitfunctions of (1) and (2) and solving for the Nash equilibrium of the product marketgame yields the following equilibrium prices and profits,
Pbr =fl+t+c, Ir br =
It is clear from the equilibrium prices that the economic effect of retentionbuilding information is to enhance the differentiation between the firms. In fact the
power of the information fl affects the equilibrium prices and profits in exactly thesame manner as the differentiation parameter t.
Equilibrium when only one party has the information
Let us now consider the product market equilibrium in which only one firm,(say firm 1), has the information. The incentive compatibility constraint is,
f3(1– x)– p l – Ix = – p2 – t(1 – x) (11)
This leads to the demand functions for firms 1 and 2 respectively as xar = x =(/3 + t – pi + p2)/(13 + 2t), while xdr =(1- xad. Solving for the equilibrium prices andprofits we get,
2fl )6p, = 3
+t+c;pd =—+t+cr 3
t + f3
2(10)
The following Proposition characterises the equilibrium contracting strategy forretention facilitating information.
Proposition 1:
Retention facilitating information is always sold under a non-exclusivecontract. The equilibrium profits of the information vendor are:
17b, 2Pb –r 966 + 2t)
14
/3(7/3 + 15t)(13)
There are two key dimensions that affect the competition between the firmsand the decisions of the information vendor: the degree of differentiation between thefirms (as captured by t) and the power of the information itself (as captured by
A. With retention facilitating information, both these dimensions have similar effectsand work in the same direction. In other words, retention facilitating information hasthe effect of increasing differentiation between the firms and increasing equilibriumprices. Consider the case when both the firms have the information. Now each firmis able to offer product modifications that protect the consumers who are close to
them. The product modification helps both firms to charge higher prices on themargin and still protect their loyal consumers. Thus the overall effect of retention
building information is to reduce the intensity of competition between the firms.
In fact, (12) shows that prices go up unambiguously for both firms even if
only one firm has the information. The firm with the information advantage is able to
1 fi get a greater market share i.e. xar = +
668 + 2t) even though it charges a price that
2
is higher than the optimal price without the modification. An interesting point is thatwhen both firms implement retention-type modifications, competition between thetwo firms is less intense and equilibrium prices (for both firms) are higher than whenonly one firm has the information. The reason for this is because the availability of
information for both the firms strategically shifts their focus from gaining marketshare (which by definition implies a reduction in prices) to taking advantage of theirloyal customer base.
This discussion highlights why the information vendor always prefers to sell
retention facilitating information under a non-exclusive contract. By shifting thefocus of both firms away from competing for market share to taking better advantageof their loyal consumers, a non-exclusive contract raises the equilibrium price andhelps better extract consumer surplus. In fact, we find that when the information
vendor uses an exclusive contract the he must actually offer the information at a price
which is lower than the optimal non-exclusive price when the information sold to bothfirms. Thus the information vendor is able to charge a profitable non-exclusive price.
Finally, profits of the downstream firms and the information vendor are
always increasing in /3 because greater power of the information works in the samedirection as differentiation and mitigates competition in the downstream market.
4.3 Conquest Facilitating Information
For conquest facilitating information (which we denote with the subscript 'c'),we begin with analysis of the product market subgame. There are number of specificregimes which characterize conquest facilitating information depending upon howpowerful the information is.
15
Case I: "No Switch Case," (0 < )6 < t)
The "no switch" case occurs when the power of conquest facilitatinginformation is weak in comparison to the level of differentiation between thedownstream firms. It is weak in the sense that the product modification (facilitated bythe information) provides a benefit to each consumer that is strictly less than theconsumer preference cost. In other words, the extent of differentiation between thefirms is relatively strong compared to the power of the product modification, so theinformation does not create a situation in which the competitor's customers switch tothe modified product.
Equilibrium when both firms have the information
When both the parties have conquest facilitating information, then the demand
functions of the two firms in equilibrium is given by the (incentive compatibility)
condition,
fix* — pi — tx* = fl(1— x*)— p2 — t(1 — x*) (14)
P2 — P1 ± t — )61 This yields Firm 1's demand function as xibc = x* = , while firm 2's2(t —fl)
demand function will be x2bc = (1-x*). Because the conquest facilitating informationis not powerful enough to overcome the disutility of the preference costs faced by
consumers who are not loyal to a firm, each firm will not be successful in inducing
the consumers who are closer to the competing firm to switch. Thus each firm only
attracts consumers who are on its part of the line. Substituting for x1 and x2 in theprofit functions of (1) and (2) and solving for the Nash equilibrium of the product
market game yields the following equilibrium prices pbc = c+ t-13.
This leads to an interesting point. When conquest facilitating information is
not very powerful (/3 <t), it is of the "no switch" variety. Contrary to the case ofretention facilitating information, conquest facilitating information reduces firmdifferentiation and the equilibrium prices. To see this notice that consumer surplus
(say from firm 1) can be rewritten as v—(t-/3)x—pi. As previously discussed, the
information does not provide firms with sufficient advantage to unanimously switch
competitive consumers. On the other hand, given that (/1 <t), the information has the
disadvantage of effectively reducing the consumer preference cost from t to (t-/3).
Thus in a sense the power of the information acts in a direction opposite to that of the
differentiation between the firms. This unambiguously reduces the "effective"differentiation between the firms and increases competition; when both firms use the
information, the overall effect is to reduce market prices. Equilibrium profits for each
16
firm are irb, = (t- f3)/2. Notice that for the "no switch" type of information an increasein the power of the information actually reduces the profits of each firm.
Equilibrium when only one firm has the information
Suppose, now, that only one of the two firms (firm 1) has the information. Theincentive compatibility constraint will be,
fix – p 1 – tx = – p 2 – 41– x) (15)
This leads to the demand functions for firms 1 and 2 respectively as
=X= P2 P1 , while Xdc =(1- xac). Solving for the equilibrium prices we getXac 2t – fi
Pac = t + c - fl/3 and pdc = t + c - 2fi/3. Thus even if only one firm has the
information, the unambiguous effect is to reduce the differentiation between the firmaand the equilibrium prices. The equilibrium profits are given by,
g"
=t P12
3 j; 71 - (lc =
2
(16)
i. 216)
32t – fi 2t – fl
As expected, the firm with the information achieves a higher profit in equilibrium.
The discussion above leads to the following proposition:
Proposition 2a:
The market for conquest facilitating information will not exist i f 0 < fi <t.
As discussed, with this type of information, the power of the information 13acts in a direction opposite to the level of differentiation t between the firms. The
shortcoming of conquest facilitiating information when (3<t, is that it is not
sufficiently powerful to "switch" competitive customers. Each firm's loyal customersare nontheless threatened when the competitor has the ability to implement a
conquesting type product modification. This forces firms to price aggressively in
order to protect their loyal consumers. The main effect of the "no switch" conquestfacilitating information is to increase competition without giving the downstreamfirms any compensating benefit.
In some sense, a downstream firm makes a commitment to not indulge in
competing for the other firm's customers by refusing an offer for conquest facilatiting
information. In the case of "no switch" conquest facilitating information, this ensures
that the equilibrium market prices are higher. In fact, the profits of a firm which
implements a conquesting modification (when 0 < fl < t) are lower than they would
17
have been without the change (to see this just compare Irk and zac with t/2). Therefore
a market for the information will not exist.To further understand this, note that if the information vendor tried to sell non-
exclusively, the profits of a firm in the non-exclusive equilibrium will be lower thaneven the "disadvantage" profits it would earn were it to refuse the information. This
can be seen by comparing gr,c with 7z-dc. Therefore neither firm accepts the offer. Nor
can the information vendor sell an exclusive contract in these conditions. A firm willreject an exclusive offer because any gain in market share due to the productmodification is more than offset by a reduction in prices.
Case 2: "Switching Case" (t < f3 < 1.5t)
Now consider conquest facilitating information that is more powerful and is in
the range (t < /3 <1.5t). .5t). The product modification provides a benefit to each consumer
that is strictly more than the preference cost incurred to buy the product in question.
Because the information is sufficiently powerful both firms have the ability to
"conquest' each other's customers. Therefore, in contrast to Case 1 above, Firm 2's
P2 - P1 + t - 11 demand function will be X2bc = x — , while firm 1 's demand function2(t – )3)
will be (1-x). In other words, the conquest facilitating information is powerful enoughto overcome the disutility of the preference costs faced by the non-loyal consumers of
a finn.Thus, in equilibrium, each firm attracts the consumers who are in the half of
the market adjacent to its competitor and the equilibrium prices are p bc = c+/3–t. Note
that the power of the conquest facilitating information still acts in a direction opposite
to the existing differentiation (t) as in the "no switch" case. However, in sharpcontrast to the "no switch" case, the equilibrium prices now increase with the powerof the information. An unusual characteristic of the equilibrium is that pricesactually decrease with lower differentiation. This is because once the information hasthe potential to "switch" consumers, greater differentiation is "bad" in the sense that itmakes the switching activity more difficult.
The analysis shows that the information vendor cannot sell non-exclusively.
If both firms use the information to implement conquesting modifications, then
competition in the market is intensified in the sense that both firms threaten to stealeach other's "natural" customers. Despite this, the resulting equilibrium prices now
could still be high if the modification was sufficiently attractive (because now the
equilibrium prices actually increase with the power of the information). However,
when fl < 1.5t this is not the case and the prices are not sufficiently high. The profits
of the firms' are less than the profits made without the modifications. As a result, oneof the firms will unilaterally have the incentive to refuse the information.
18
In the same vein, neither is an exclusive offer of the information possible. Ifwe assume that a firm could use the information exclusively, it will potentiallythreaten to capture the other firm's most loyal customers. As discussed before, thisthreat leads the firm without the information to protect its loyal customers by reducingits price leading to "too much" competition. The following proposition summarizesthis discussion.
Proposition 2b:The market for conquest facilitating information will not exist if t < )6 < 1..2.
The two propositions 2a and 2b deliver the consistent message that a vendorwill find it impossible to sell conquest facilitating information that is not sufficiently
powerful or in markets with sufficiently strong differentiation. In these markets theeffect of conquest facilitating modifications is to effectively increase price
competition between the firms. In contrast, retention facilitating information can
always be sold. This suggests that product modifications that are directed to a firm's
loyal customers might be more common.
Case 3: Switching Case (1.51 < 11 < 21)
The following proposition characterises the information vendor's contractingstrategy when conquest facilitating information becomes even more powerful. As inCase 2, when both firms purchase information under a non-exclusive offer and
implement the corresponding conquest facilitating modifications, they will "conquest'
each other's customers at an equilibrium price ofp bc = c+/3-t. Each firm is willing to
pay fi - 3Y for the information yielding a total profit to the vendor of 2 )6 - 3t .2
However, in contrast to the previous case (i.e., fi < 1.50 the exclusive offer
now has a significantly different effect on the market outcome. The information now
is so powerful that the equilibrium outcome in the downstream market is one in which
the firm without the information is foreclosed from the market. It must be noted thateven though the firm without the information is a non-operating firm (in that it sells
nothing), the exclusive buyer of information is by no means a monopoly. Thepotential competition from the non-operating firm still affects the price that theexclusive buyer of the information can charge and the equilibrium price in the
downstream market is c+ fl-t. This also implies that the vendor's exclusive selling
price will be /3-t. A comparison of the non-exclusive and exclusive profits leads to
the following proposition:
Proposition 2c:When 1.5 t < )5' <2t, conquest facilitating information will be sold exclusively.
19
In sum, when conquest facilitating information is sufficiently powerful, it hasthe potential to allow a firm with exclusive possession of the information to lockoutits competitor. This makes the exclusive contracting strategy attractive for theinformation vendor.
Case 4: Switching Case (fl > 2)
Case 4 considers the information vendor's contracting strategy for the case inwhich conquest facilitating information is even more powerful in relation to the extentof differentiation between the downstream firms. As in Cases 2 and 3, when both
firms purchase the information under a non-exclusive offer and implement the
corresponding conquesting modifications, they will "conquest" each other'scustomers. The following proposition characterizes the optimal contract for this case:
Proposition 2d:
For conquest facilitating information characterised by fa > 2, the information vendor
is indifferent between using the exclusive or the non-exclusive strategy.
Suppose the vendor uses an exclusive contract. With extremely powerful
information, the firm that gets the exclusive use of the information will be able to
charge a higher price and still switch its competitor's customers. However, the abilityof the exclusive buyer of information to take advantage of the powerful information
and charge a higher market price is tempered by the fact that this high price might
result in a possible loss of its loyal customers. Recall that the loyal consumers of afirm are less affected by the conquest facilitating modification. This obtains because
the firm without the information would retaliate by lowering its price and therebycould become more attractive to the exclusive buyer's loyal customers. It is the fearof losing its own customers that prevents the exclusive buyer of the information fromtaking full advantage of the information. Therefore, the exclusive sale price will notincrease commensurate with the relative power of the information. In contrast, if theinformation is sold non-exclusively then firms tend to be less worried about theirback-yard loyal customers as both the firms would now be motivated to switch thecompetitor's customers. As a result, each firm focuses on the customers located on
"the far half of the market" and competition at the margin is less intense. This makes
the non-exclusive contract as attractive for the vendor as the exclusive contract.Given that the model is indifferent between the two types of contracts, the choice
of which contract to use would then hinge on implementation factors such ascontracting costs and costs of enforcement. Between the two, exclusive contracts are
more likely to be subjected to contracting and enforcement hazards. There might bepositive costs to drafting exclusive contracts that clearly outline both the penalties forbreach and nature of the exclusivity being contracted. For instance, the case of
Adolph Coors Company and Molson Breweries regarding an alleged breach of an
20
exclusivity agreement indicates that exclusive contracts can lead to destructiveconflict between partners and costly legal battles12.
4.4 The Choice of Which Type of Information to Sell
Consider now the situation in which the information vendor were able todesign the information packet such that it be used either for building loyalty (retentionfacilitating) or attacking the competitor's customers (conquest facilitating). Whatfactors govern the type of information that the vendor would desire to sell?
Proposition 3:
When an information vendor can choose the form (i.e. retention facilitating or
conquest facilitating) of his information, the vendor prefers to sell retention
r-facilitating information when
3t< + 1) and conquest facilitating information2
otherwise.
At low levels of 13 relative to the differentiation between the firms, conquest
facilitating information cannot be sold at all, so it is not surprising that theinformation vendor prefers to sell retention facilitating information. Retentionfacilitating information is always profitable and is always sold non-exclusively
because it effectively increases the amount of differentiation in the market. Thisallows firms to reduce price competition and thereby benefit from higher prices thatprevail.
3t r-At levels of fl > — (,,15 + 1) , conquest facilitating information yields greater
2
profit in spite of the fact that higher prices are always associated with theimplementation of retention facilitating modifications of the same impact i.e.
Pbr=13+t+c versus per= f3-t+c. This obtains because once /3 becomes sufficiently highrelative to the differentiation between the firms, switching competitive consumersbecomes easier. This increases the attractiveness of conquest facilitating informationfor the downstream firms and increases their willingness to pay for such information.
Proposition 3 implies that the information vendor will tend towards themarketing of retention facilitating information in highly differentiated industries and
when the resulting product modifications are not very powerful. The vendor is more
likely to sell conquest facilitating information in markets where the degree of
differentiation between firms is small and when the information is more sophisticated
and powerful. In these markets, a vendor of information can benefit by creating asituation in which firms effectively "swap" customers.
12 Details of this dispute are discussed in the "Molson hit with Hefty Damages", Globe and Mail,Toronto, October 21 1996, B1-2 and Wells, J. (1997).
21
5. Closing Discussion
5.1 Managerial Implications
The preceding analysis provides useful insights into the market forinformation that is used to guide product modifications of downstream firms.Specifically, the model has useful prescriptions for managers that are in the businessof selling information they already possess and for managers that can tailor andmodify information to make it useful for downstream purchasers of the information.
The first and perhaps most useful insight of the model is that an informationvendor has a much easier task if he is in the business of providing information that is
generally used to retain or build loyalty with the existing customers of a firm. First,the information will always have a market regardless of its expected impact and
second, the information should always be sold non-exclusively (or broadly within a
category). As a result, there is never a need to write formal exclusivity contracts forretention facilitating information.
A second implication pertains to the attractiveness of offering exclusivecontracts for product modification information. A vendor never has an interest to
offer exclusivity if information is used for retention facilitating modifications.Moreover, it is only for moderately attractive conquest facilitating modifications i.e.,
for PE {1.5t, 2t}, that exclusivity can enhance profits. For conquest facilitating
information that has higher impact, a vendor can make just as much money by sellingthe information non-exclusively. This highlights an interesting point. In the existingresearch on information in financial markets (eg., Grossman and Stiglitz 1980,Admati and Pfleiderer 1986), there is a strong notion that the information vendormight increase the value of the information product by restricting the sale to a few of
the potential buyers. Our analysis suggests that information in product markets mightbe generally biased towards non-exclusive sales even though (as in financial markets)
exclusivity enhances the value of the information product. The presence of product
differentiation in product markets seems to bias the information market towards non-exclusive contracts.
5.2 Conclusions and Future Research
Product modifications are a common component of the marketing mix
strategies of firms. In addition, many organisations are now selling informationwhich is a "by-product" of their primary activity and which facilitates product
modifications. Yet no research exists which examines the market for such
information. This paper analyses how such product modification information affects
the competition between downstream firms and also the optimal contracting strategiesfor an information vendor. We trace the type of contracting strategy to two factors:
22
the degree of differentiation in the downstream industry and the power/impact of theinformation.
We find that the optimal contracting strategy for retention facilitatinginformation is to sell non-exclusively to both competitors. With retention facilitating
information the impact of the information is in the same direction as productdifferentiation. Therefore the main effect of retention building modification is toincrease the differentiation between downstream firms and thereby, reduce pricecompetition.
We find that conquest facilitating information cannot be sold unless themodifications it facilitates are large in relation to the degree of differentiation in theindustry. For conquest facilitating information, the impact of the information acts in adirection opposite to the differentiation between the firms. Conquesting type
modifications have the effect of reducing differentiation in a category and increasing
price competition. Therefore it is not until the information is powerful enough to
allow foreclosure of the firm without the information, that a market will exist for this
type of information. When it is possible to sell conquest facilitating information,exclusive contracting is useful. An interesting finding that also emerges is that theinformation vendor will become indifferent between an exclusive and a non-exclusivecontract in the extreme case of highly powerful information.
A final finding concerns the type of information that we should expect aninformation vendor to offer given that he has the ability to tailor the information for
either retention building or conquesting type modifications. When the level of
differentiation in a category is relatively strong and the information is not very
powerful, we should expect the information vendor to focus on the sale of retention
building information. In contrast, in more competitive industries with relatively lowdegrees of differentiation, the vendor is likely to sell conquest facilitating information.The sale of conquest facilitating information is also more likely when the impact ofthe information is high relative to the level of differentiation.
There are two interesting issues for future research. One aspect that we do notexplore in this paper is the cost of implementing the modifications themselves. We
assume that modifications can be made costlessly and that a modified product is
produced at the same marginal cost. An interesting extension would be to examinehow the vendor's ability to sell the information is affected by implementation costs.
Another issue that we leave to future research is that of competition in the information
market. If information vendors first had to make decisions of which type of
information to collect, an important question is whether we should see differentiated
or identical vendors and how is this affected by the degree of differentiation in the
downstream market.
23
References
Admati, Anat R. and Paul Pfleiderer (1986), "A Monopolistic Market forInformation", Journal of Economic Theory, Vol. 39.400-438.
Arrow, Kenneth J. (1962), "Economic Welfare and the Allocation of Resources forInvention", in The Rate and Direction of Inventive Activity, ed. R. Nelson, PrincetonUniversity Press, 609-626.
Blattberg, Robert C., Rashi Glazer and John D.C. Little (1994), "The MarketingInformation Revolution," Harvard Business School Press.
Chang, Chun-Hao and Chi-Wen Jevons Lee (1994), "Optimal Pricing Strategy inMarketing Research Consulting", International Economic Review, Vol. 35, No. 2(May), 463-478.
Colombo, Richard A. and Donald G. Morrison, (1989), "A Brand Switching ModelWith Implications for Marketing Strategies", Marketing Science, 8, 1 (Winter), 89-106.
Green, Paul E. and V. Srinivasan (1990), "Conjoint Analysis in Consumer Research:Issues and Outlook", Journal of Marketing, Vol. 5, September, 103-123.
Grossman, Sanford J. and Joseph E. Stiglitz, (1980), "On the Impossibility ofInformationally Efficient Markets", American Economic Review, 70 (June), 393-408.
Hauser, John R. and Steven M. Shugan, (1983), "Defensive marketing strategies",Marketing Science, 2, 4 (Fall), 319-360.
Kotler Philip and Gary Armstrong (1996), "Principles of Marketing," Prentice Hall,Engelwood Cliffs, New Jersey, 291.
Lilien, Gary L., Philip Kotler and K. Sridhar Moorthy (1992), Marketing Models,
Prentice Hall, Engelwood Cliffs, New Jersey, 245-248.
Preston, Lee E. (1994), "Territorial Restraints: GTE Sylvania (1977)", in John E.Kwoka, Jr. And Lawrence J. White, eds., The Antitrust Revolution: The Role ofEconomics, HarperCollins Publishers, New York.
Samuelson, P.A. (1947), Foundations of Economic Analysis, Harvard UniversityPress, Cambridge, MA.
24
Samuelson, P.A. (1954), "The Pure Theory of Public Expenditure", Review ofEconomics and Statistics, Vol. 36, 387-390.
Samuelson, P.A., (1955), "Diagrammatic Exposition of a Theory of PublicExpenditure", Review of Economics and Statistics, Vol. 37, 350-356.
Sarvary, Miklos and Philip M. Parker (1997), "Marketing Information: A CompetitiveAnalysis", Marketing Science, Vol. 16, No. 1, 24-38.
Soberman, David A., "Optimal Marketing Strategies for Static Information", Working
Paper 97/25/MKT, INSEAD, Fontainebleau, France
Tirole, Jean (1990), The Theory of Industrial Organization, The MIT Press,Cambridge, Massachusetts, 282-287.
Wells, J. (1997), "Thirst for Growth: Molson tries to halt a decline in beer sales",Macleans, September 1, 44-45.
25
Technical Appendix for Contracting for "Retention" and "Conquest" FacilitatingInformation
Proof of Proposition 1Retention facilitating information is always sold under the non-exclusive
contract. The equilibrium profits of the information vendor are:
/7,r, 2P, -r 9(fl + 2t)
Proof:
Using the equations in the paper. The exclusive profit is 11„, = 7Car - Thdr =13/3.
The non-exclusive profit is the minimum of 2(nar - and 2(7rbr- nth .). Using the
equations in the text rcar - niir= 4+2(3/3)2/03+20A/2 and 7tbr - 7tdr= f3(713+150/63+20/18.
Assume that 2(76 - ni,r)< 2(nbr - ndr)•
2218t+ —
3 ) t < (7 + 150 /32
/3 +2t 2 1866 + 18(fl + <0
which is impossible since the numerator and denominator are both positive.
Therefore, 2(7tbr- Cdr) is the minimum of the two terms. Now we show that 2(knbr ndr)
is strictly greater than is Assume not:
> fl(7)3+150 1 7fl+15t
3 9(6 + 2t) 3fl+6t
4 1g + 9t <0
which is impossible. Q.E.D.
Proposition 2a:
The market for conquesting information will not exist i f 0 < f3 < t.Proof
When 0<f3<t, a necessary condition for exclusive selling is that the buyer
(who makes 7Cac after implementing the modifications) have profit greater than 7Cnc.
This condition is necessary or else the buyer is better off refusing the exclusive offer
(since he knows that his competitor will also refuse to buy the information). Using the
equations in the text,
fl(7 f3 + 15t)
13(t - fl) 7rac — –2t – fl
For all 13<t, the denominator is positive but the numerator is negative for all r3<3t/2.
Therefore, the term nay nix is negative and the information cannot be sold
exclusively.
Similarly, the non-exclusive profit is the minimum of 2(7tar 7Cnc) and 2(7cbc - ndc). As
above the term,negative so the information cannot be sold non-exclusively.nac - Inc is
Q.E.D.
Proposition 2b:
The market for conquesting information will not exist if t < < 1.5t.
Proof
The proof of this proposition is analogous to the proof of Proposition 2a
because the terms mac and niic are the same (only the term ltbc is affected by the
switching which occurs at these levels of p). Q.E.D.
Proposition 2c:
When 1.5 t < /3 <2t, conquesting information will be sold exclusively.
Proof
Step 1:
To determining ?Lac and ltd , we first solve the simultaneous optimization problem for
both firms. Equilibrium demand and prices are:
1 fi fi 2)3
X = , plc = t + c , p c = t + c –2 6(2t –,(3) 3 3
At levels of p>1.5t, this solution is associated with negative demand and prices less
than marginal cost for the firm that does not have the information. Therefore, the
modifications are sufficiently powerful when 13>1.5t such that the firm without the
information is forced from the market.
Step 2
Assume that the equilibrium is a corner solution in which the firm with the
information sets price at 13-t+c. At this price, the firm without the information cannot
attract any customers, even at pricing at marginal cost (since the surplus for the
2
customer at x=1 is R from both firms, any customer located at a position where x<1
will strictly prefer the offering from Firm 1).
We now show that Firm 1 has no incentive to change its price. The profit function for
the firm that has purchased the information and implemented the modification is
gac = x* p it ac = 1* (fi —t+ c) when the firm prices at 13-t+c. A drop in price
will not increase its demand and will simply lower its profit. Therefore the firm that
has implemented the modification will not drop price below 13-t+c.
We now consider a rise in price. In this region,
x . P2 — Pi ±tg =
p2 — pl+t* (pi c)
alt.ac =
p2 -2pi +t + c= oac
2t — )6 2t — fi al,' 2t — fi
This generates the reaction function for Firm 1: p1 = (p2 +t + c)I 2 . Similarly,we
obtain the reaction function for Firm 2 (the firm that has not implemented the
modifications): p2 = (p, + t — ,6 + c) / 2 . Sketching these functions quickly reveals
that they do not intersect in the region where p i >13-t+c. The intersection is at (pi, p2)= (t+c-p/3, t+c-2(3/3). Choosing any candidate price greater than 13-t+c is not stable
and using the concept of rationalizability (in the sense of Bemheim, 1984 and Pearce,
1984), the equilibrium is (p i , p2) = ((3-t+c, c). Thus, the equilibrium under an
exclusive sale results in a market outcome where the firm implementing the
modifications gets the entire market and a profit (n.) of P-t+c. The firm not buying
the information makes zero profit.
Step 3
As per the discussion in the text, when both firms implement conquesting
modifications, they effectively swap customers when 13>t. Thus, x --0,1 — p2 + t -
,0/2(t-fl)
and 1-x=(p2 — pi + t - f3)/2(t-/3). But in contrast to the usual problem, the objective
functions for each firm are gl, = (p, — c)(1— x) and 71-2,, = (p2 — c)x due to the
swapping of customers. Solving the resulting system of equations generates the
following solution:
x* = —1
g 1c = 7r2c =
fi —t 2 , AC = P2c = fl—t+c,
2 •
3
Step 4
Using the information above the profit from selling exclusively is 11. = nayadc=13-t.
The non-exclusive profit is the minimum of 2(1tac-icnc) and 2(7tbc-7tdc). Substituting for
nac-nno we obtain fi – 3t for nbc-nac, we obtain 13– t . For all values of f3<2t,
2 2
fi – —3t
<L3– t
Therefore, the non-exclusive profit is 213-3t. For all values of2 2
1.5t<13<2t, P-t is greater than 2P-3t therefore selling exclusively is more profitable.
Q.E.D.
Proposition 2d:
For conquesting information characterised by /3 > 2t, the information vendor is
indifferent between using the exclusive or the non-exclusive strategy.
Proof
Following from Step 4 above, the non-exclusive profit when fl > 2t is 2(7Cbc-
'luck). This is 134, identical to the profit made from selling the information exclusively
to one firm. Q.E.D.
Proposition 3:When an information vendor can choose the form (i.e. retention facilitating or
conquest facilitating) of his information but not its impact (i.e. /3), the vendor prefers
to sell retention facilitating information when /33t
< (V5 +1) and conquest2
facilitating information otherwise.
Proof
For all 13<1.5t, conquest facilitating information cannot be sold. In contrast,
fi(7 + 15t)iretention facilitating information generates a profit of which is always
9(fl + 2t)
positive. This confirms the proposition for 13<1.5t. When 1.5t<13<2t, the conquest
facilitating information generates an optimal profit (exclusivity) of f3-t. When 13>2t,
the conquest facilitating information generates optimal profit of 134 regardless of the
form of contracting. Assume that retention facilitating information is more profitable
then:
4
)6(7 16 +15t) 1-11„>13-t. Substituting, we obtain > f3 – t . This implies after some
9(fl + 2t)
manipulation that /3 E {_ _3t (v3- _ 1), _3t2
2 (J + 1) for this inequality to be satisfied.
The first term in the range is clearly negative and the second term is greater than 2t (it
is approximately 4.85t). Thus, the range where 13>2t is divided into the region
2t, 3t (J + 1) where retention facilitating information is more profitable and a{2
3t r-second region, )6 > — (-4 5 + 1) , where conquest facilitating information is more
2profitable. Q.E.D.
Technical Appendix References
Bemheim, B.D. (1984), "Rationalizable Strategic Behaviour", Econometrica, Vol. 52,1007-28.
Pearce, D.G. (1984), "Rationalizable Strategic Behaviour and the Problem ofPerfection", Econometrica, Vol. 51, 1029-50.
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