Tilburg University

Boundedly rational decision emergence

Güth, W.

Publication date:1997

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Citation for published version (APA):Güth, W. (1997). Boundedly rational decision emergence: A general perspective and some selective illustrations.(CentER Discussion Paper; Vol. 1997-48). CentER.

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Centerfor

Economic Research

No. 9748

BOUNDEDLY RATIONAL DECISIONEMERGENCE - A GENERAL PERSPECTIVE AND

SOME SELECTIVE ILLUSTRATIONS-

By Werner G~th

June 1997

ISSN 0924-7815

Botnidedly R.ational Decision EmergenceA General Perspective and Some Selective

Illustrations~-

Werner Giith~

1~Zay 22, 1997

Abstract.

For a restricted class of decision problems a general framework is out-

lined specifying how boundedly rational decision makers generate their

choices. Starting from a"~laster Adodule" which keeps an inventory of

preciuuslv successful and unsuccessful behavioral rotttines several submod-

ules can be called forth which either allow to adjust behavior quantitatively

(by "l~irection~l Learninp" and "Adaptat-ion Procedurè') or qualitatively

(by "Cugniti~'e Updating" ), or to generate new decision routines (by apply-

in~ "New Problem Solver"). Our admittedly bold attempt is validated by

relatiuK our theoretical constructs to some selective stylized experimental

results.

`I grati~Fldly acl:nowleclge helpful commeuts by Eric van Daunne as well as the encouragement

h}' Reinhard Sa~lteu. Financial support by the Deutsche Forschmtgsgemeinschaft (SFB 373) isgratefuLly arknowledged.

t(CentER, T'ilburg Uni~-ersity, RO. Box 90153, 5000 LE Tilburg, Netherlands), Htunboldt-Universitc ot' Berliu, Department of Ecottotnics, Institute for Economic Theory III, Spandauer

Str. 1, D- 101 ï8 Beslin, Gennany.

1. Introduction

~~íore and mure it becomes clear that human decision makers can at best be

boimdedlv ratiunaL One good example to demonstrate the practical impossibility

uf ratiuual deciaion rnaking is chess, with its finite but - for human decision makers

and modern chess computers - much tou large variet.y uf board situations. For

oconomic ~~Loic~~ situatii~r~s simila,r problenLS can resi.ilt (see, for instance, the at

first. sight rathi~r ~~,~til- saving decisioiis in Anderhub et al., 1996).

It is, of course, easy to criticize withont offering sonrething new. A lot is known

about honndedly rational decision behavior. One central idea is, for instance, to

rechice the nniltiplicity of goals and to measnre the achievement of the remaining

goals in riiscrete steps, the so-called aspiration levels, i.e. to substit.ute the neo-

classical liypofliesis of opt-imizing by satisficing (Simon, 1976). There aze models

of aspiration adaptation (e.g. Sa.uermann and Selt.en, 1H59, and, for bilateral bar-

{;aiiung, ~I~ietz. 19n8). Therr. i~ evidence thnt people often rely on pa.5t c'xperiences

ir~stead of purely forward ]ooking rational considerations (e.g. t.he so-called surdc

cost-fallacies) and that inessential aspects (the frame or the presentation of a sit-

uat.ion) c~isi inHuence behavior dramatically by awakening different concerns (see,

for instance. the decomposed prisoners' dilemma experiments b,y Pruitt, 1967, and

the more~ general stndies inspired by Tversky and Kahneman, 1986).

Still, the inairv pieces (of the complex mosaic) do uot. provide a complete picture of

the theoi,v of boundedly rational decision making. We t.oo often rely on part.icular

aspects, e.g. on avoiding to rlecide repeatedly by committing once and forever to

certain priu~~iples líke reciprocit,y (Fehr et al., 1993), on aspiration adaptation in

concessi~~in baigaining like Tiet.z (1988), and on directional learuing in repeated

decision making, e.g. Selten and Btichta (1~J94). What is urgently needed is

some general perspective how some or hopefully - the most important facts

abouf buuudcd rationality can be combined into a dynamic rnodel of decision

emergence.

1

Here we make a bold attempt to develop such a dynamic model of decision erner-

gence which is partly speculative in nature and partly supported by empirical,

most.ly experirnental evidence. When trying to model the decision dynamics we

sometirnc~ti cannot avoid some speculation although most of the reasoning should

be~ rathr-r uatural.

In order to limit the degree of speculating about boundedly rat.ional decision

emergence we narrow the scope of possible decision situations. On the one hand,

we typically envisage choice problenrs with ordered choice sets, e.g. subsets of the

real nunrhers. On the other hand, we want to abstract from choice problerns where

one invests in learning how reasonable a choice is, e.g. by successive proposals in

case of concession bargaining (see Tieta, 1988). This list is, however, not complete.

Further restrictions will be rnentioned when they are needed. ~Nhat we suggest

is only a general frame of boundedly rational decision emergence. For a general

algorithmr rnuch more has to be known how people clecide and how t.hey combine

their various routines of making a decision. We may never come that far.

Exantpl~ for such simple choice problems exist in abundance. A consumer, for

instarrce, is usually asked how nmch he is going to buy of certain products. Ex-

perímental studics of individual decision making often confront participants with

risky choice problems - the so-called lotteries assigning positive probability to

more than just one outcome which the subjects can either sell (willingness to

accept-studies) or buy (willingrress to pay-studies). Clearly, determining a price

above which one wants to sell or below which one wants to buy falls into the

category of choice problems for which we want to outline the dynamic process of

decision emergence. Stating such a price is a problem of selecting a value from

some orríereci set, here a subset of the real numbers, and there is no way of learn-

ing which price is best if one has only one unit to sell or to buy (see Camerer,

1995, for a survey of such experimental studies).

~ Notice, however, that neo-classical theory or game theory doe:; not offer a general algorithmeither. Ouly when knowing the preferences of all pazties, their beliefs, how it is ~nentallyrepresented etc. - in general the complete normative model - one can derive the solutionbehavior. To find out these aspects for all possible decision problems will ne~-er be possible.

~

Example,ti in iuteractive decision rnaking are whai an allocator or proposer offers to

the recipient(s) in the dictator or iiltinratum garne (see~ Rot.h, 1995, for a survey).

Our rti5sumptions do not rrtle out that such a garne is repeated with the same or

new partners. Here, however, we want t.o exclude for the sake of simplicity that

an allocator or proposer can try various offers in order to learn how the recipient

reacts tu t3imn. Snch explorations would necessarily infíuence tu~d rnost likely

complicate the cogiutive dvnanric process of making one's offer.

To illustrate that our assumptioirs do not rule out repeat.ed interaction one type

of exrunplr~ to which we refer is of this form. More specifically, we will discuss

fïnitsly repcatod prisoners' dilemnra experirnents, e.g. as studied hy Selten and

Stiicker (19ti6) with binary choiccs in t-he base game, as well as finitsly repeated

public good provisiorr-games where one usually has more t.han two ordered choice

alternatives, e.g. the integer amounts of tokens invested in the public good (see,

for instance, Felir und G~chter, 1996).

An attempt will be made to ilhrstrate how our general model of decision emergence

can be a-pplied to decision making in those azrd some related experirnent.al choice

problenrs. C'onversely, the Frvidence of such experimental studies will more or less

explicitly guide the design of certain crucial espects of our general model.

In the following two sections we first describe the "M~ster Moduld' and then

its submoduhs to wtvch it refers. Section 5 then discusses various experimental

choice problems in light of the general model which were selected to illr~strate its

various snbmodules. The Concluding Renrarks discirsses how our pc~rspective for

developing gencral theories of boundedly rational decision ernergencc is related to

other approaches.

2. The master module

An important aspect of tnrman decision making is that we are not born as grown

up decision makers. Notice, however, that the traditional view in evolutionary

3

biology (see, for insta.nce, Maynard Smith, 1982) and in evolutionary game

theory (sc~e the survey by Hammerstein and Selten, 1994) assumes that all es-

sential choices are genetically determined, i.e. already made when being born.

This may be true for some basic instincts like crying when hungry, thirsty or hurt

which we want to neglect. For the choice problen~s we have in rnind, the way

of how a decision emerges can depend, however, ou mauy phenotypical aspects

which oue can surnmarize under the heading of cultural evolution. Notice that

cultural evolution is b,y no means restricted to the hunran world. The same kind

of apes living in sinrilar environments, for instance, may or may not develop as

nut crackers which requires a lot of teaching and training.

Developing as a decision maker typically means to rely on previous experiences.

The "Master ?t-lodulé', described as flow chart in Figure IL1, therefore assumes

that one first. checks the behavioral repertoire (sec~ also Guth, 1995) in order to

gain from former experiences. The behavioral repertoire could be seen as a

collection of goocí and bací decision rules, possibly qualitative and quantitative

ones, for certain classes of choice problems, e.g. for buyïng a used commodity

like a second band car from somebody unknown. Notice that after the decision

one usually tries to check whether or not the choices made were reasonable. Such

an ex post-consideration may, of course, result in post-decisional regret which,

in our view, can be very meaningful. It improves the behavioral repertoire in

the sense that in future one will shy away from such unreasonable choices. As a

matt.er of fact it is the behavioral repertoire of highly experienced decision makers

what justifies the~ir higher income in spite of the fierce competition on the market

for top managers.

Figure II.1 i~l5ert here!

A new decision problem, especially sorne of the experirnental choice problems, e.g.

the evaluat.ion of lotteries with unambiguotrsly defined payments and objective

probabilities, ma,y not closely resemble previous choice problerns. According to

Figure IL 1 the cíecision maker will then apply the submodule "New Problem

Solver" which will be described below. Whether or not a new decision problem is

4

"similar" to a previously experienced one is judged by referring to the cognitive

model, developed for the previous decision problem. If all struct.ural relationships

of the cognitive model are present in both situations, they can be viewed as

similar. If such a resemblance exists, it may, however, be only a qualitative one.

In competitive bidding with randornly deternrirred private values the bidder may,

for instance, have experienced only other private values than the present one.

If so, he is assumed to apply the "Adaptation Procedure" whereas he can rely

on "Directional Learning" (see, for instance, Selten and Buchta, 1994) when the

privat.e value remains constant.

Notice the very natural sequencing of resernblance checks according to Figure IL1.

One first looks at a class of situatiorLS which are qualitatively equal, e.g. two first

price auction choices with different private values. Remember that qualitative re-

semblance has to rely on cognition. Two decision problenrs aue perceived as qual-

itatively similar if their cognitive representations contain the sarne structural

relationshipsz. Only when such a qualitative resemblance exists, one investigates

also the quantitative similarity of the new choice problem and the previous ones.

Quantitative similarity should be defined in view of the promineuce slructure of

open and closed scales (see, for instance, Albers and Albers, 1983, Rubinstein,

1988, and Tversky 1977) which rnight very well depend on the cout.ext (when

numbers measure c~o-probabilities rather than monetary units, an increase from

99 to 100 appears more essential). In general, quantitative sirnilarity can prevail

even in case of minor quantitative diHerences.

One may want to rely on a more complex `:Master Module". Here this has not

been done in order to limit the degree of speculation. In our view, an attempt

to outline t.he dynamíc process of decision emergence should be based on sound

experiences of human decision making. And, of course, the cornplexity of the

"Master Modtile" is determined by the complexity of its three submodules to

which we now turn our attention. Our few selective illustrations (see section 4

below) will hopefully illustrate that the main structure of the "Mtister Module"

ís ernpirically sound. A more refined "Master Module" should rely on further

empirical evidence.

2The fact that a certain decision routine will be only applied, when situatious are at least

qualitatively similar, ~nakes them domain specifla Since what is seen as qualitatively similar

depends on its mental representation, this allows for individual differences in the domains of

certain routines what mi[;ht account Eor individual differences in behavior.

5

3. The submodules

When de;cribing the submodules we proceed from more to lESS spccific resem-

blance, narnely frorn qualitative and quantitative via purely qualitat.ive ones to

not even yualitative ones. Thus the order of the submodules is "Directional Learn-

ing", then "Adaptation Procedure", ancí finally "New Problem Solver" which is a

slightly ui~~re complex submodule.

3.1. Directional Learning

One confronts qualitatively and quantitatively the same choíce problem, for in-

stance, in experiments where one repeat.edly plays t.he same game with new part-

ners. Notice that playing repeatedly with the same partners may be seen as an

entirely different. choice problern. Here one might rely on a grand plan for the

whole futiire like "to start with cooperation and an intention to deviate from

cooperation towards the end" in repeated prisoners' dilemrna experiments with

the sanre partners. If such a repeated game with the same partners is played

repeatedl,y with changing partners, "Directional Learning" can, of course, again

be applied (see, for instance, Selten and St~cker, 1986, who explore repeating a

repeated game with new partners).

Unlike in evolutionary game theory people's decisions are not genetically or cul-

turally determined, but usually based on some basic cognitive model relating

the - likelv outcome t.o one's own choice variable. In a first price-auction

one will, for instance, be aware of the fact that a higher bid will increase the

probability of winning, but also what one has to pay, namely one's own higher

bid, in case of winning. To balance the two effects would, however, require to

quantify them what might overburden a boundedly rational decision maker. Here

"Directional Learning' offers an alternative by simply adjusting behavior in the

direction of those choices which would have been good in past decisions (see Selten

and Buchta, 1994, for an application of directional learning to repeated first price

auctions with changing partners). Notice, however, that "Directional Learning"

G

requires sonre cognitive model by which one can assess ex post whether or not

another decision would lrave been better (in a first price-auction with an ex post

given highest competing bid one needs to assess oue's own payofi for other own

bids what requires an tnrderstanding of the payoff schedule).

There are rnany ways how such a basic cognitive model can develop, e.g. by

accepting other persorLS' views, or by applying one's own "New Problem Solver".

Here we do not want to discuss this in more detail. Wha~t is importa,nt is that such

a cogrritive model exists by which one can ex post-evaluat.e past decisions if one can

observe them (see Figure IIL1 describing the submodule "Directional Learning").

Notice tha.t some celebrated learning models (see, for instance, R.oth and Erev,

1995) do uot at all rely on cognition, but rather assume t.hat people tend to

repeat those choices more frequently which, in the past, were more rewarding -

somet.imes this is called reinforcement or stimulus response-learning.

There may be rare situations, e.g. when hardly anything is known or highly sto-

chastic arrd complex decision taslcs discouraging any atternpt to uuderstand tlrc

likely effects of one's own actions by reduciug complexity, where one may rely on

stimulus respouse-learning at least initially. Botmdedly rational decision makers

will, however, cont.inuotLSly tr,y to develop simple cogrutive ideas to understand

why certain choices imply certain results. Thus behavioral adaptation by rein-

forcement is more relev~-urt for small children who are not yet trying to understand

the world or for cognitively less developed species of t.he animal kingdom as well

as for some rare human decision problems.

Figrrre III.1 insert here!

"Directional Learning" is sometimes restricted to repeated decisions with observ-

able outcomes (see, for instance, Selten ancí Buchta, 1994) where ouc always can

check whether there would have been a better choice. If there exist many better

choices, the selection of one of th~e remains open (one only goes into the direction

of a better choice). This shows that no cornplete algorithm is offered. There are

certain choices for which we do not state how they ernerge simply because we still

do not understand the dynamic processes of generating them thorouglily enough.

7

For the sake of completeness Figiue IIL1 also includes repeated choice making

where the results allow to disprove the basic cognitive model. For this case the

submodule "C;ognitive Updating" in Figure IIL2 describes how a decision maker

adjusts to the experience that his cognitive ideas are at odds with what happens.

The basic idea uf Figure IIL2 is that of a hierarchy of cognitive models as suggested

by Gut1i (1995). One iLSUally turr~s attention to more complex aud cognitively

more denianding models only when it becomes evident that simpler models do

not comply with the facts. Of course, t.he more demanding considerations have

to be maiiageahle.

It should be pointed out that the final step in Figure IL1 may alsu include more

general evaluations than just whether the c.hosen alternative passes an ex post,

evaluation based on one's own cognitive model. One may, for instance, learn that

"Directional Learning" results in poor success if compared with other ways of

improving behavior, e.g. coiLSUlting experts. And that may be well kept. in mind,

e.g. by remernbering to consult an expert next time instead of trying to improve

behavior by `'Directional Learning".

Figure IIL2 ii~sert here!

3.2. Adaptation Procedure

Unlike in "Direct.ional Learning" where one repeatedly encounters the same choice

problem allowing to quantitatively adjust one's behavior at least in the right direc-

tion, "Adaptation Proc.edure" is applied when there is only a vague resemblance of

the new and the previously experienced dc~cision situations. One example would

be a first pric~~auction with a new private value. But the resemblance could

also be more dramatic: The bidder may, for instance, have experiences with first

price-auctions, but not with second price-auctions or first and second price-fair

division garnes where the price is distributed among the bidders instead of being

given to seller (seca Giith, 1996, who compares the bidding behavior in all four

bidding problems). Whereas in the first case the first question in Figure IIL3 will

be confirnred, in the latter case it probably will be rejectecl although the two - at

first sight - structurally different bidding problems cíiffer in only one parameter,

namely how much one participates in the sales price.

Adapting behavior t.o parameter changes in case of qualitatively similar choices

may not be always easy. In the case of first price-auctioris oue might simply rely

on the same proportion of underbidding in the serLSe of 6~ - ve . b;'wo where 6;

is the new bid, v; the new private value and óow; the underbidding coefficient

recommended by previous experiences with ~~o. When, however, bidrling with true

value v~ iu a first price - fair division garne instead of an auction one might warrt

to change the degree of underbidding, e.g. by overbidding. Here we refrain from

elaboratiug "Adaption to Chauged Paranreters" as a further submodule. How this

will or shoulrí be done by bomrdedly rational decision makers rnay often depend

crucially on the context and how it is cognitively perceived. As in "Directional

Learning" one might orily specify the direction of adaptation and leave it open

how far one adapts what migld depend ou the prorninence structure (Alhars s,nd

Albers, 1983).

Figure IIL3 insert here!

In case of essential quantitative differences or when a bad decision would be very

costly, e.g. in case of major investrnent choices, Figure IIL3 denies that one bases

one's decisiou on such a poor resembla,nce. Thus one tackles the choice problem

in essence as a newly arising decision ttr.5k to which the submodule "New Problem

Solver" applies which will be described in the following section. Li other words:

Dramatic quantitative differences will be treated like qualitative ones.

3.3. New Problem Solver

Facing a decision task for which one has no resembling experiencE~ - not nec-

essarily own oues, but. also no resembling experiences by others of whom one is

y

awaze - is defirritely the most challenging task when generatíng an una[nbiguous

choice }~y boundedly rational consicíerations. Examples of such situat.iorrs are rare.

wP usually encounter choice problerns wlrich either we ourselves or others have

experienced before. An aircraft having to land on an icescraper with no food

for the survivors except for the dead budies of those whu did not survive may

result in such a new ancí unpleasant choice problem: should one try to save one's

own life by "cannibalism" in spite of all moral obstacles? Also some experimental

situatiorLS appear like rather unusual choice problenLS, e.g. the reciprocity game

stucíied by Berg, Dickhaut, and McCabe (1995). You harcíly ever receive a large

pa,yment from somebod,y who cíoes not know you and whorn you do not know at

a1L If so. it usually will not be tripled and one does not often have the chance to

pay him something back.

In general, Figure IIL4 is an attempt to generalize the more specific approach for

generatiug ultimatum offers (Giith, 1995 b). It starts by determining the basic

concerns - in case of ultimatrnn offers how much one gets in case of agreement

and the chances of an agreement. Often - like in ultimatum bargaining - the

basic concerns are obvious although different individuals with different experiences

might disagree about this, e.g. in dictator giving some people might care for the

wel]-being of the recipient(s) whereas others might. develop such an interest only

after learning that others care or after experiencing or imagining the frustration

felt by recipient(s).

In ultimahnn bargaining a cognitive rnodel by which one can check whether basic

concerrLS are conflicting is nat.rrrall,y a model of responder behavior. Guth (1995

b), for instance, sugg~ts a range of offers which surely will be accepted as well

as a ra.nge of offers which surely will be rejected what. does not exclude an in-

termediate rauge uf offers where one is not sure at a-11 how likely they will be

accepted. Of course, this implies that the two basic concerns are conHicting since

the "unacceptable" offers are the ones which, in case of acceptance, yield more to

the proposer.

Fluther questions to be resolved before a decision emerges relate tu the cost of

a bad decisiou. In case of high costs one will not mind to invc~t more effort. in

10

finding out what seems to be a"safe" decision, respectively in checking competing

models for ttieir recommendation.

Figure II[.4 irLSert here!

4. Application to some experimental choice situations

The outline of decision emergence giveu above is mostly based on reasonable

subrnodtiles with supporting empirical evidence. But it. is far from providing a

widely applicable algorithm by which one can predict which choices will be made.

Nevertheless it is, in our view, an important step in combining various pieces of

what is known about boundedly rational decision making. To demorrstrate its

potential the general model will be applied to sorne selective experirnental choice

problems.

4.1. Evaluating lotteries

A lottery L can be described as au l-vector

L - (P I ~~)~~;~~

of l (monetary) prizes P~ as well as their realization probabilities P; with pl ~- ... -F

p~ - 1. Coi~sicíer the following mechanism (Becker, de Groot., and Marshak, 1963)

for selling such a lottery L: A prize p E [p, p] with

pGP,cj~fori-l,...,1

is randomly drawn. If the seller's bid b exceeds p, he does not sell and earns

nothing, otherwise he sells the lottery L at the random price p. Clearly, optimality

11

reqtrir~ to bid truthfullV, i.e. the bid b should be the price at which one is

indifferent between selling and not selling.

But what is obvious in view of norrnative theorv mav not be true for bound-

edly rational cíecision makers. They will not know the price at which they are

indiffereut between selling and not selling and they may not understand that

the mechanism is incentive compatible, especially so in case of unusual or infre-

quently tracíed "commodities": Guth and Weck-Hannemarm (1997), for instance,

have asked voters to sell their voting right in such a way. Except. for convinced

non-voters one will hardly tneet an individual who readily knows t.he value of its

voting right.

When t-rying to generate the bid b for selling the lottery L the "Master Module" in

P'igtrre IL 1 first checks for related experiences ancí what has been learnt from them.

Here we want to focus on somebody with no similar experiences who therefore

has to apph' the "New Problem Solver" in Figure IIL4.

According to Figure IIL4 one has to find out one's basic concerns, i.e. the conse-

quences about which one cares. Since nobody else is concerned ( the experimenters

playing the role of potential buyers), the basic concerns are the rnonetary earnings

a.nd t.heir probabilities. Relating these basic concerns to the bid h to be submitted

is already quite demanding. Since there may be many random prices a person will

refrain from considering all possible earrrings and how their likelihood is influenced

by the own bid. !~fore realistically a bidder may try to determine bounds for his

bids b. Sincc one receives P,~ in case of the p,-probability event and not selling,

the bidder will see that bidding b~ P2 for i. - 1, ..., l or b G P,~ for i- 1, ..., l

can only result in lower monet.ary earnings. To generate a bid within the range

P c b C P of the lowest. ( P) respectively largest ~P~ monetary prize P requires

a more specific cognitive model.

Assume the following qualitative cognitive model: a higher bid 6 increases the

average price p in case of selling, but. decreases the probability of selling. F~om

such a rather crude analysis one may conclude that basic. concerrrs are conflicting

12

although tht~y am uot since there exists an wtacnbiguously best bid G if one knows

the owu trui~ va,lne of lottory L. This detnunstratas that a norutat ivoly trivial

decision prol~lem may appear very difticnlt if inadequatcly perceived. What is

uormatively inceattive cotupatible tnay not be behaviorally incentive compatible.

Figure IIL4 su~gests to ask whether or not a bad experience is very costly. If

not, one sitnply may choose a bid 6 reduciug the pussible amount of frustration.

F`rnstration from selling would be measured by the positive ~tmouttts P- p

whereas frustration from not selling wotild be caused by positive amouuts

p- P atistuniug that onc, observes the random price p eveu when not selling. In

case of jnst two prizes P and P with 0 c P G P the bid

6--I' f P

~

would, f~rr inytance, raducc stich frtL4tr~ition ~s f~u as possible.

Prospect theory (Kahnetuau aud Tversky, 1979) is cliHicult to apply since there

seems tu l~e no obvions reference poiut. from which to ute~LSUre i;ains and losses.

One mit;ht ~~onsider the own bid as one. Bnt since the bid determines only a

border between two price ra.ng~ aud is unlikely to be the actual price, t.his may

not. be very c~onvincinfi.

Unlike iu ueucla~ssical theory a theory of boundedly ratioual decision utaking can-

not simply asstune that an individual knows at which price or bid the losses from

selling will outweigh those from not selling. We do not claim to have a satisfying

answer to this probletn which, in our view, is closely related tn forrnin~~ an initial

aspiration expressing for the case at hand what a decision maker will want to

receive iu returu for his loktery L. Such an initial aspirat~ion level will not, only

express what L promises to him, but also what he wants to gain from selling it.

Incentiveti of thc latter kind explain the frequently obsetved endowment effects

(see, for in,ta.nce, Kaluieman, Knetsch, and Thaler, 1990), namely that potential

sellers state ttigher bids thati potential buyers although cudowments are allocated

1;3

randomly. Experimental effects like preference reversals (see Selten, Sadrieh and

Abbink. 1995, for a recent study and Camerer, 1995, for a sruvey) illustrate that

in spite ~tf the many experimental studies no clear answer has ,yet been found.

The need to evaluate lotteries also results when one rnust choose between lotteries

(see Selten, Sadrieh artd Abbink, 1996, for a recent study and Camerer, 1995, for

a survey of experimental studies). A special case of such a decision problem is

~rheu one lottery guarantees a certain prize, i.e. if one of the lotteries is of the

f~,nu

L-(P~p;P~l-~r) withpE[0,1].

~~hen choosing between L and

G'-~P'~P,P~I1-P~ withP'cPcP~andOc~i cl,

one can define the gain of L' as P~ - P, occurring with probabilit,y 1-P and the

loss of L' by P- P' whose probability is p. In view of I{ahneman a,nd Tversky

(1979)'s prospect theory' the sure profit P of L serves as a reference point when

evaluating the prospects, implied by L'. Accepting the typical experience that

losses matter twice as rnuch as gains, one would choose L' rather than L if

2(1 -~i) ~P~-P~ 1~i (P-P')

or

1-P' P-P'2 ~ ~~,-P.

3Comparing this choice between two special lotteries with the earlier problem of stating aborder b for selling a lottery with many prices illustrates that prospect theory is applicable only

in a narrow dumain.

14

i.e. if the ratio of the ]oss and gain of L', as compared to L, is not too large.

When coufrouting such a choice for the first time - since such clearcut alternatives

are rarely observed in reality, it most hkely will be in an experiment - this cognitive

process ("in case of L I know what I get. why dou't I look at what L' promis~

me in comparison to L and try to evaluate these gains and losses"?") could be

easily reconciled with t.he submocíule "New Problem Solver" in Figure IIL4 (the

gain and loss of L being eompeting concerns and the higher evaluation of losses

resulting frorn the additional causal relationship thcct losses matter more).

4.2. Bidding when former experiences are misleading

In the second price-private value auctiorrs it is optimal (the only we~kly undom-

inated strategy) to bid t.ruthfull,y (Vickrey, 1961). Having experienced such an

aucti0n uften does not necessarily generate truthful biclding (see, for instance,

Giith, Schrnittberger, and Schwarze, 1983). If one, however, explains that over-

and underbidding one's true value ca,nnot improve the result, but may result in a

loss, the proportion of essentially truthful bids increases dramatically (see Giith

and Schwarze, 1983).

Consider now an individual whose experiences with second price-auctions resulted

in tmderstanding and accepting that truthful bidding is reasonable. How will

such a decision maker, whose behavioral repe~rtoire (see Figure IL1) recommends

truthfi~l bidding in second price-auctions, generate his bid when confronting a

second pricE~fair division game where the price is distributed equally among all

bidders (see Giith, 1996, for an experimental stucíy)? One possibilit;y, on which

we want to focus our attention, is that one accepts, accorciing to Figure IL1, the

close resernblance of both bidding situations with the resu]t of bidding truthfully

in second pricafair division games where such behavior is less reasouable.

What we want to illustrate here is how "Directional Learning" can finally lead to

"Cognitive Updating" and to a bidding behavior which is more appropriate for

1J

second pricc: fair division games. Let us consider that the bidder ha-s submitted

a truthful bid b ~a-hich is second highcst (and thus determining the price), but far

below the highest bid b(assuming that at least. the two highest bids are publicly

announced). The ex post:evaluation, required by Figure IIL1. will tell him that a

higher bid 6 in the range 6 c b c 6 would have granted liim a better result, namely

b~n instcad of h~n. with n. denoting the number of bidders. Such a conchision will,

of course, que~stion the cognitive idea that neither over- nor underbidding one's

true value can improve the result, i.e. the bidder will then turn to "Cognitive

Updatin~~ at~cording to Figure IIL1.

According to Figrne IIL2 an attempt to adjust. one's cognitive ideas will typically

be a search for neglected causal relatiorLShips. For the et~5e at hand a re.~sonabfe

causal relatiorrship is that the own bid b does not only define the interval of prices

p) b where one refrains from buying and of prices p c b where one wants to buy,

but. can also determine what one receives in case of not buying. Actually from

including the latter aspect one ma,y understand that in second price-fair division

games it can be reasonable to overbid one's true value. Clearly such a more

complex cognitive model can account for the former experience that overbidding

would have baen better. The bidder will t.herefore (see Figure IIL2) return to

"Directioual Learrung" by which he, in view of his updated cognitive model, can

improve lus bidding behavior in repeated second price-fair division games.

4.3. Dictator giving

Dictator giving naturally arises when (with some valuable commodity, c.g. money)

well-equipped individuals are confronted with some less favorabl,y enclowed indi-

viduals. ylost forn~s of charity clearly fall under this category. Usually those who

are better equipped will have earned t.heir relatively better endowment, e.g. by

own previous efforts. Thus the - mostly psychologica] - experiments of reward

allocation, e.g. by Shapiro (1975) and IVfikula (1977), are far better studies of

dictator giving since they (try to) induce entitlement (one is "entitled" to one's

working share) whereas in the experiments by economists (see for a rare example

Hoffman and Spitzer, 1985) roles are too often allocateci randomly.

16

To illustrate the differenccs between rewa~rd allocation and dictator games with

randonily ~cssigned roles consider an individual who played several dictator gasnes

and lea.rned what is rather likely in case of no ent,itlement axxd no double blind-

ness (see Bulton and Zwick, 1995, as well as Hoffman, McCabe, Shachat and

Smith, 1991) - to share equally. Assume that this individual now becom~ the

allocator in reward allocat.ion where the monetary amount c to be distributed is

substantial ancl, furthermore, it is thc result of some se~rious efforts to which he

himself contributed onl,y a share s with 0 G s c 1 where we assume that all indi-

vidual efforts are comparable. In our view, such an incíividual will answer the first

question iu Figure IL1 by "Yes", but rnost likely deny the close resernblance of re-

ward allocat.ion and his previous experiences with dictator games. This then leads

to the application of the "Adaptation Procechxre" in Figrue IIL3, especially when,

in case of just two individuals, the deviation ~ s- 1~2 ~ from equal coutributions

is large.

Many will dex~Y the first quPStion in Figure IIL3 and aii,swer the second one by

"Yes" since participants in reward allocation cxperiments wit.h s c 1~2 usually

demand only s-c for themselves what. is very rare in dictator games with randonrly

assigned roles where one would nat.urally suppose s- 1~2. Of course, an indi-

vidual may view qualitative differences between reward a.llocation a,nd dictat.or

games as essential. According to Figiire II.1 he then will apply "New Problem

Solver".

Figure IIL3 does not deny the possibility that an individual, who has experienced

equal sharing in cíictator ga,mes, will continue to do so in rewasd allocation. Ac-

cording to the rasults of Mikula (1977) this is most likely Eor s? 1~2 and minor

efforts. But there is definitely the possibility that ~ne denies the close resemblance

of the two situations of dictator giving, ~nost likely by paying attention to one's

contribution share s when ~ s- 1~2 ~ is non-negligible.

17

4.4. Ultimatum proposals

Will applying the "New Problem Solver", described in Figure IIL3, to ultimatum

proposaLS differ from its application to dictator givin~? It has been argued in

Giit.h (1995) that there is a basic concern of ultimatum proposers, namely the

desire to have one's proposal accepted, which is not present in dictator garnes.

Naturally the cognitive model will have to account for this basic concern. In our

view (see alsci Giith, 1995b), an ultimatum proposer will try to predict how a

typical responder will react. This must not be a complete responder strategy. It

rLSUally will sufHce to knocv some proposals which will surely be accepted, e.g. the

equal split, ancí others where one is almost sure of a rejection. What a proposer

then finally proposes will depend on his other concerns. If he is mainly interested

in his owu well-being and if the "cake" - the monetary amount to be allocated -

is large, he will tc:nd to choose the highest almost surely accepted proposal, e.g.

by asking for two thirds of the cake. If by imagining how a responder will react he

has developed a basic concern for the responder's feelings or if the cake is rather

small, he ma,y refrain from any risk of conflict and suggest an eGual divísion of

the cake.

One should notice t.hat, in principle, there may be three basic concerns, the mone-

tary win of the proposer him5elf, the probability by which a proposal is accepted,

and the well-being or the feelings of the responder. At least in t.he usual range of

ultimatum oHers (to the responder), which do not exceed half the cake size, there

is no confíict between the latter two concerns: A greater offer will improve the

well-being and the positive feelings of the responder and also increase the proba-

bility that he will accept the offer. Thus the basic conflict of ultimatum proposers

is the tracle off between a higher monetary own demand and its detrimental ef-

fects on the responder who becomes angry when receiving an "unfair' offer. As we

know (see Roth, 1995, for a survey) even a considerable, but. nevert.heloss unfair

offer will not prevent an angry responder from punishing the proposer.

So the major difference of the cognitive models in dictator giving and ultimatum

proposing is not the concern for the other player, but only that it has no strategic

12i

aspect in dictator giving, whereas it crucially det.ermines the likelihood of an

efficient agreement. in ultirnatum proposing. As a consequence a dictator can

rely only on kris owu feelings of what is just whereas an ultimatmn proposer will

seriously take into account, how others might react.

In view of Figure IIL4 one thus can suffer from competing basic concerns also in

dictator giving, but view a"bail experience" as not very costly since the proposal

cannot be rejected. In ultimatum bargaining where a proposal can be rejected,

"bad experiences" are usually very costly what results in incorporating additional

cat~sal relations, e.g. in the form of predicting responder behavior (see Figure

III.4).

4.5. Playing repeatedly

Repeated games a.rc defined by a base game, e.g. t.he prisoners' dilemma, and a

repetition number 1' where we assume thal all former movec are made public C)f

course, all experimental studies have to relv on finite repetition numbers T in the

sense that it is commonly known t.hat t-he game will be played at most T times.

Here we are interested in experinrents of repeated games since they provide an

easy way of introducing more complexity.

From man,y experimental studies of repeated strategic interaction (see Roth, 1995,

for a survey) with the sarne group of individuals playing t.he base garne repeatedly

it is well-known t.lrat people start playing with rather vague intentions for later

repetitiorLS. In a 20 times repeatedly played 2 person-prisoners' dilenuna experi-

ment a part.icipant usually starts by playing cooperat.ively wit.h a vague intention

to deviate from continued cooperation towards the end. When this will actu-

ally occur is probably only determined when the end is near - a decision mostly

emerges when it. is nceded, i.e. when one is pressed to decide. If, furthermore,

one pla,ys the repeated ga.me repeatedly (usually with changing partners in suc-

cessive repeat.ed experiments), the end or termination effect (the number of

later periods without mutual cooperat.ion) will be very likely adjustsd in view of

"Directional Learning" (see the pioneering study of Selten and St~cker, 1986).

19

Repeating repeat.ed garnes adds even more complexity to the decision problem.

Let us therefore concentrate on experiments where a repeated game is played just.

once, i.e. the same group of individuals plays the base game T tirnes. Many such

experimeuts have either rLSecí the prisoners' dilemma where a player can choose

to defect or to cooperate or the private supply of public goods where a player

can contribute any part of his private endowment, e.g. any integer number of not

more than 2O tokerLS. According to Fehr and G~chter (1996) participants in a 10

times played public good-provision game typically start out by cont.ributing rather

much and end by contributing significantly less. Thtrs the stylized facts from such

studies are cíeclining contributions over time and neither maximal eontributions

at the beginning nor mirrimal contributions at. the end.

How can such facts be explained by our general model for decision emergence?

It seems reasonable that the artificial set up of an exactly T times played public

good-provision game will not resemble any previous experiences, i-e. according to

Figure IL1 one will have to apply the "New Problem Solver". One then must ask

for the bz~tiic coucerns in the repeated game and try to relat.e them. In our view,

this will typically be done by first exploring the basic concenrs in the base game.

How will one then develop acognitive model as reqrrired by Figirre IIL4Y The likely

result of such an analysis is that. one is aware of the conflict between one's own

interest and what is good for the group. Most participants will, furthermore, see

it as an advautage that they do not play the base game just once, but repeatedly.

What one will easily see is that cooperative results - a high level of individual

contribution.5 - can be stabilized by the explicit or implicit threat of punishing

deviators. So the coguitive rnodel for the repeated game might assume that most

pla,yers will aim initially at a high level of cooperation and that one has a chance

to punish deviatioiLS from cooperation. How to regain a high level of cooperation

after punishing deviators may not be explicitly considered by boundedly rational

part.icipants. Clearly, such considerations can explain why pa.rticipants are willing

to contribnte a lot when beginning to play a public good-contribution game.

During thr~ cuurse of a finitely repeated game the chances to punish deviators

and, of coirrse, aLso to regain cooperation tliereaft.er are decreasing. Thus the

20

cognitive structure, outlined above, predicts less stable cooperation when the end

of interaction is uear. In our view, this explains why the level of cooperation

decreases over time.

What is more difficult. to explain is why the average contribution of even the last.

period is atill significantl,y positive. In our view, such results incíicate that the

level of cooperation or the group efficiency is a ba5ie concern of at least some

participants. Such a basic concern may come up already when analysing the base

game (eveu in one shot: experiments one oft.en observes some contributions). It

may be strengt.hened or awakened when a group of individuals is playing the base

game repeat.edly. Furthermore, achieving a high level of cooperation in previous

rounds may result in some group coherence and, in consequence, in a new basic

(group) concern of what the group in total achievES. In our view, only such a

basic intc~rest in the group's success a5 such can explain why some participants

contribute a]ot in the last round although they seem to be aware that there can

and will be some freeriding.

5. Concluding remarks

Our aim was to provide on overall picture how decisions of botmdedly rational

decision makers emerge. Any such attempt will suffer from two major risks:

One is to aim at a possibly perfect algorithm which, however, would be overly

speculative due to the limited knowledge about. bounded ra.tionalit,y. We have

tried to account for this risk by restricting the variety of decision problems and

by not fully specifying all details. But, of cor~rse, even this does not sicffice to rule

out any specillation.

The other risk is to neglect icnport.ant facts about bormdedly rational decision

behavior. Here we may point out that some important aspects like, for instance,

the processes of aspiration adjustment (see the early study by Sauermann and

Selten, 1959), of balancing aspiratior~s (Tietz, 1988), and of learning (e.g. Roth

and Erev, 1995) may simply be versions or - when infornration is very scarce

21

- alternatives of "Directional Learning" as dcscribed in Figure IIL1. Similarly,

other aspects of boundedly rational behavior, e.g. post-decisional regret which,

at first sight. nray appeat even irrational, can be accomodated into our general

model. But, of course, the author is also not aware of all t.he (social) psychological

and economic stucíics which might have helped to provicíe an empirically more

profound and thus more acceptable model of decision emergence.

If, however, sorne celebrated concept is not explicitly considered here, this is often

due to the fact that ít is at odds with our general perspective, especially of viewing

decision makirrg as a dynamic process. Let us consider, for instance, prospect

theory (ka,luremau and Tversky, 1979) which ~rssunres that decision makers know

how to evaluate gair~s and losses in view of a given reference point. Of course,

people must and will evaluate gains and losses and it is often true that losses

count more. But they do not have an evaluation function readily available which

they simply can apply. In section 4.1. we have seen how complicate it may be to

generate a bid for selling a cornplex lottery. Although it is applicable in special

"domaiiLS', it is cíifficult to see how prospect theory can help to generate choices

in more genera] decision problems.

An example of a concept which is more implicitly included in our general frame-

work is that one of a decision frame (Tversky and I{ahneman, 1986) which,

in our view, can infiuence strongly how a situation is cognitively perceived. The

framing of a decision problem might even lude true and indicate wrong qualita-

tive resernblance (see Figure IL1). It certainly infíuences which additional c.ausal

relationships one considers in "Cognitive Updating" (Figure IIL2) and whether

qualitative differences are seen as essential (Figure IIL3). But again the dynamics

are important: Somebody who has repeatedly played the ultimatum game in a

neutral frarne might be less likely to yield to a"charity frame" of the same game

as somebody who confronts such a decision problem for the first time.

How can one defend our bold attempt t.o develop a cornprehensive model of bound-

edly ratiunal decision emergence in spite of how little is known about bounded

rationality xiid of the author's limited knowledge? The excuse is that we need to

~,~

pnt together the more or less independent pieces of what is known about bounded

rxtionalit,v. Aud somebody who would be aware of tuu many possibly relevant

ideas may lie simply be overburdened by putting them all into perspective. Like

iu real life ~.~nisidering too many tLSpects may be detrimental. We necd complex-

ity reduction also iu science boundedly ratioual scientists generate theories as

people gen~~r~ite decisioitis.

There will hop~~Eully be other approaches pursrung siinilar goals. Thcir ideas

should be p~utly qiute su7ul~u-. And it will finally be an empirical ducstion which

approarli is hetter. By oiu admittedly bold attempt we only hope to initiate

a uurtu.~lly huitful exchauge Low to develop a genera] framework of boundedly

rational de~~ision cmergence; we do not claim to know the fiiial answer.

If there is not stilficient evidence this does not mean that one is purely specu-

lating. lu thc~ tradition of two former approaches (Guth, 1995 and 1',)95b) many

of the theorctical construct~ of our general inodel can be related to stylized facts

of empiri~~ally mostly experimentally - observed boundedly rational decision

makíng. Of ~~ourse, one finally will have to substituto "loosely relating theoretical

cor~structs tu stylized facts" by rigid statistical tests of fimdamental hypothe-

ses. At present there are far too rnaiiv imderlying hypotheses wluch would need

such a profound ~~rnpirical validation. ~Vhat one can hope for is that after a dis-

cussion ahont the general fraanework of boundedly rational decision emergence

researchers will try to locate their specific research within such a general diagram.

This might theu clarify many ~LSpects and greatly reduce thc degree of speculation

about bounded rationality.

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27

Decision,needed,

Dces behavioral repertoirecontain a qualitativelysimilar choice problem?

~Yes

~ -Is the situation alsoquantitatively similar?

~No

Apply~Iew Problem` Solver"! ~

Apply"Adaption

Procedrrre"

~ Perform `rx post-evaluationifpossible and store

experience inbehavioral repertoire

~Yes

Apply"Directional

n.~B i

Figure IL1: The Master Module of decision emergence ( submodules needed: "NewProblem Solver". "Adaptation Procedure", "Directional Learning")

Chooae wéet would have bem gaod`inviaw ofprevious'

ex posFavduetionl

Tcan,rou onee~ve therosults of the decision?

No . . Yee

,Did yrna casutó~pove7

PcaeaveI

` rd., x.:. 1.~ .N.:I.w..i

'.,.~ "„d.....- W ~auce effeds7model ae om with - -queehooable tollablly:

, go back b'Meafec Modole"1 ` ~ ~

No Yee

~Rrill you hsve iochooee apm?

1

No 1

rOflen emugh7

PraeerveYwa oo~i4v~

model on whirb youan bue e: posFevehuboo;go barJc Lo "Meeter Module"I

Figure 1[L1: The submodule "Directional Leaming"Isubmodule needed: "Cognitive Updating")

Application`neededr

FCan additional causalrelationship' explain whyresults have not improved?

~Yes

additionalrelationship in

Include

your cogmuve moaei;,go back to "Master Module"!

Figure IIL2: The submodule "Cognitive Updating" ( ~`: causal relationships are consideredaccording to their cognitive complexity by applying simpler before moredemanding ones)

Application`neededr

TAre the quantitative differencesessential based on your intnitionofquantitative resemblance?

INo

~Yes

1Is a bad experiencevery costly?

INo )

Relyon cognitive

model for previonslyexperienced situation to

adapt' to quantitative differences;go back to "Master Modnle"!

~Yes

~ ApplyTiew Problem

Solver"!

Figure IIL3: The submodule "Adaptation Procedure"(submodule needed: "New Problem Solver",': e.g. in the form of "DirectionalAdaptation" specifying only the direction in which one adapts)

~wn~~,~t~~~

TDevelop co~itive modol m

celaoe ywQ besic`caocane m yaa'

decisiaoi

7 - ~ -Aro yaa óasic ooncame ma9ir.tmgiu view of yac co~itive madeiT

No .

.- - -I~Moomox dePcodaro ~ooadiogM yo~c oo~itive model?

.Ya

1 -

Qioore16e e~eme;

go bact m"Mae[er Module"I

Chooeewhá serme

se5e ~nd reeeooablein vbw of yav madd;

go óacJc io "MeaOer Modub'1

. Ya

Choooe `wLst ód~ar

yrnv badc caoca~ia view of yaa oo~itive

model: ~o b~rJc b `bleeta Module"

,L a bsd spaieooe~~

would.ddmaat cmlmlatiomehip~ yield diffaent4sde ofó of ba~c caoc~dl

~ ~Ya

Figure 1[L4: The submodule "New Problem Solver" (~: causal relationships are consideredaccording to their cognitive complexity by applying simpler before moredemanding ones)

No. Author(s)

9G75 M. Das and A. van Soest

9G7G A.M. Lejour andH.A.A. Vcrbon

9G77 B. van Aarle andS.-E. Hougaard lcnsen

9G7R Th.E. Nijman, F.A. dc Roonand C.Vcld

Title

A Pancl Data Model for Subjective Information on Household[ncome Growth

Fiscal Policies and Endogenous Growth in Integrated CapitalMarkets

Output Stabilization in EMU: Is There a Case for an EFTS?

Pricing Term Structure Risk in Futures Markets

9G79 M. Dufwenberg and U. Gneery Efficiency, Reciprocity, and Expectations in an ExperimentalGame

9G80 P. Bolton andE.-L. von Thadden

9G81 T. tcn Raa and P. Mohncn

9GR2 S. Hochguertel andvan Scest

9G83 F.A. de Roon, Th.E. Nijmanand B.J.M. Wcrkcr

9G84 F.Y. Kumah

9G8~ U.Gneezy and M. Das

9G8G B. von Slcngcl,A. van dcn Elzen andD. Talman

9G87 S.Tijs and M. Kostcr

9G88 S.C.W. Eijffinger,H.P. Huizinga andJ.J.G. Lcnuncn

9G89 T. tcn Raa and E.N- Wolff

9690 J.Suijs

9G91 C. Seidl and S.Traub

9G92 C. Scidl and S.Traub

9G93 R.M.W.J. Beetsma andH.lcnsen

Blocks, Liquidity, and Corporate Control

Thc Location of Comparative Advantages on the Basis ofFundamcntals only

The Relation betwecn Financial and Housing Wealth of Dutch A.llouscholds

Testing for Spanning with Futures Contracts and NontradedAssets: A General Approach

Common Stochastic Trends in the Current Account

Experimental Invesligation of Perceived Risk in Finite RandomWalk Processes

Tracing Equilibria in Estensive Games by ComplementaryPivoting

General Aggregation of Demand and Cost Sharing Methods

Short-Tcrm and Long-Term Govemment Dcbt andNonresident Interesl Withholding Taxes

Outsourcing of Services and the Productivity Recovery in U.S.Manufacturing in thc 1980s

A Nucleolus for Stochastic Cooperative Games

Rational Choice and the Relevance of Irrelevant Altematives

Testing Decision Rules for Multiattribute Dceision Making

Inllation Targets and Contracts with Uncertain CenValBartker Preferences

No. Author(s)

9G9d M. Voomcveld

9G9í F.B.S.L.P. Jansscn andA.G. de Kok

9G96 L. Ljungqvist and H. Uhlig

9G97 A. Rustichini

9698 G.Gurkan and A.Y. ~zge

9G99 H. Huizínga

96100 H. Huizinga

96101 H. Norde, F. Patrone andS. Tijs

96102 M. Bcrg, A. De WaegenacreandJ. Wiclhouwcr

96103 G. van dcr Laan, D. Talmanand Z. Yang

96104 H. Huizinga and S.B. Niclsen

96105 H. Degyse

96106 H. Huizinga and S. B. Nielsen

96107 T. Diccl:mann

96108 F, dc long andM.W.M. Dondcrs

9G109 F.Vcrboven

961 10 D. Granot, H. Hamersand S. Tijs

961 I 1 P. Aghion, P. Bolton andS. Fries

96112 A. De Waegenaere, R. Kastand A. Lapicd

Title

Equilibria and Approximate Equilibria in Infinite PotentialGames

A Two-Supplicr Inventory Model

Catching up with thc Kc}ncsians

Dynamic Progamming Solution of Incentive ConstrainedProblcros

Sample-Path Optimization of Buffer Allocations in a TandemQucue - Part 1: Theoretical Issues

The Dual Role of Money and Optimal Financial Taxes

The Taxation Implicit in Two-Tiered Exchange Rate Systems

Characterizing Properties of Approximate Solutions forOptimization Problems

Optimal Tax Reduction by Depreciation: A Stochastic Model

Esistence and Approximation of Robust Stationary Points onPol}topes

Thc Coordination of Capital Income and Profit Taxation withCross-Owmershíp o( Firms

Thc Total Cost of Trading Belgian Shares: Bmssels VersusLondon

The Political Economy of Capital Income and Profit Taxation ina Small Opcn Economy

The Evolution of Convcntions with Endogenous Interactions

Intraday Lead-Lag Relationships Betwecnthe Futures-,Options and Stock Market

Brand Rivalry, Markct Segtnentation, and the Pricing ofOptional Engine Power on Automobiles

Weakly Cyclic Graphs and Delivery Games

Financial Restructuring in Transition Economies

Non-linear Asset Valuation on Markets with Frictions

No. Author(s)

9G I 13 R. van den Bririlc andP.H.M. Ruys

9G114 F. Palomino

961 IS E. van Damme andS. Hwkens

96116 E.Canton

9701 J.P.J.F. Scheepcns

9702 H.G. Blocmen andE.G.F. Stancanclli

9703 P.JJ. Hcrings andV.J. Vannctelbosch

9704 F. dc Jong, F.C. Drostand B.J.M. Wcrker

9705 C. Femández and M.F.J. Steel

9706 M.A. Odijk, P.J. Zwaneceld,J.S. HooghiemsVa, L.G. Kroonand M. Salomon

9707 G. Bekaert, R.J. Hodrick andD.A. Marshall

Title

Thc lntemal Organization of the Firm and its EvtemalEmironment

Conflicting Trading Objectives and Market Efficiency

Endogenous Slackclberg Leadership

Business Cycles in a Two-Sector Model o( Endogenous Growt}t

Collusion and Hierarchy in Banking

Individual Wealth, Reservation Wages and Transitions intoEmployTnent

Refinemcnts of Rationalizabilil~~ for Nomial-Form Games

E~changc Ratc Targct Zoncs: A New Approach

On the Dangers of Modelling Through Continuous Distributions:A Bayesian Perspective

Decision Support Systems Help Railned to Search for `Win-Win' Solutions in Railway Nctwork Design

The Implications of First-Ordcr Risk Aversion for AssetMarket Risk Premiums

9708 C. Fernández and M.F.J. Stcel Multivariate Student-i Regression Models: Pitfalls and Inference

9709 H. Huizinga and S.B. Niclscn

9710 S. Eijffinger, E. Schaling andM. Hcebcrichls

9711 H. Uhlig

9712 M. Dufwenberg and W. Guth

9713 H. Uhlig

9714 E. Charlier, B. Melenberg andA. van Soest

Privatization, Public Im~estmcnt, and Capital Incomc Taxation

Central Banl: Independence: a Sensitivity Analysis

Capital lncome Taaation and thc Sustainability of PermanentPrimary Deficits

Indirect Evolution Versus S[rategic Delegation: A Comparisonof Two Approaches to Explaining Economic Institutions

Long Tertn Debt and the Political Support for a Monetary Union

An Analysis of Housing Expenditwe Using SemiparametricModels and Panel Data

9715 E. Charlicr, B. Melenberg and An Analysis of Housing Expenditwe Using SemiparamctricA. van Soest Cross-Section Models

9716 ].P. Choi and S.-S. Yi Vertical Forecloswe with the Choice of lnput Specifications

No. Author(s)

9717 J.P. Choi

971R H.Degryse and A. Irmen

9719 A. Possajennikov

9720 J.Janscn

9721 !. ter Horst and M. Verbcek

9722 G. Bekaert and S.F. Gray

9723 M. Slikl:er andA. van den Nouweland

9724 T. ten Raa

972~ R. Euwals, B. Melenberg andA. van Scest

9726 C. Fershtman and U. Gneery

9727 J. Potters, R. Sloof andF. van Windcn

9728 F.H. Page, Jr.

9729 M. Berliant and F.H. Page, Jr.

9730 S.C.W. EijffingerandWillem H. Verhagen

9731 A. Ridder, E. van der Laanand M. Salomon

9732 K. Kultti

9733 J. Ashayeri, R. Heuts andB. Tammel

9734 M. Dufwenberg, H. Norde,H. Reijnierse, and S. Tijs

9735 P.P, Wakker, R.H. Thalerand A. Tverslry

9736 T. Offcrman and J. Sonnemans

Title

Patent Litigation as an Infortnation Transmission Mechanism

Attribute Dependence and the Provision of Quality

An Analysís of a Simple Reinforcing Dynamics: Learning toPlay an "Egalitarian" Equilibrium

Regulating Complementary Input Supply: Cost Correlation andLimited Liability

Estimating Short-Run Persistence in Mutual Fund Performance

Target Zones and Exchange Rates: An Empirical Investigation

A One-Stage Model of Linl: Formation and Payoff Division

Club Efficienc}' and Lindahl Equilibrium

Testing the Predictive Value of Subjective Labour Supply Data

Strategic Delegation: An Experiment

Campaign Expenditures, Contributions and DirectEndorsements: The SVategic Use of Information and Money toInfluence Voter Behavior

Existence of Oplimal Auctions in General Em'ironments

Optimal Budget Balancing Income Tax Mechanisms and theProvision of Public Goods

The Advantage of Hiding Both Hands: Foreign ExchangeIntcrvention, Ambiguity and Private Information

How Larger Demand Variability may Lead to Lower Costsin the Newsvendor Problem

A Model of Random Matching and Price Formation

Applications of P-Median Techniques to Facilities DesignProblems: an Improved Heuristic

The Consistency Principle for Set-valued Solutions and aNew Direction (or the Theory of Equilibrium Refincments

Probabilistic Insurance

What's Causing Overreaction? An Experimental Investigation ofRecency and the Hot Hand ECfect

No. Author(s)

9737 ?~l.~ Kabir

9738 M. Das and B. Donl:ers

9739 R.J.M. Alessie, A. Kapteynand F. Klijn

9740 W. Guth

9741 I. Woiltiez and A. Kapteyn

9742 E. Canton and H. Uhlig

9743 T. Fecnstra, P. Kort andA. de Zeeuw

9744 A. De Waegenacre andP. Wala:er

9745 M. Das,1. Dominitz andA. van Scest

974G T. Aldershof, R. Alessie andA. Kaptey~n

9747 S.C.W. Eijffingcr,M. Hocberichts and E. Schaling

9748 W. Gulh

Title

Ncw Evidence on Price and Volatility Effects of Stock OptionInlroductions

How Certain aze Dutch Households about Future Income? AnEmpirical Analysis

Mandatory Pensions and Personal Savings in the Netherlands

Ultimatum Proposals - How Do Decisions Emerge? -

Social Interactions and Habit Fortnation in a Model of FemaleLabour Supply

Growth and ihe Cycle: Creative Destruction VersusEntrenchment

Em ironmental Policy in an [nternational Duopoly: An Analysisof Fcedback Investment SVategies

Choquet Integrals with Respect to Non-Monotoníc Set Functions

Comparing Predicitions and Outcomes: Theory and Applicationto Income Changes

Female Labor Supply and the Demand for Housing

Why Money Talks and Wealth Whispers: Monetary Uncertaintyand Mystique

Boundedly Rational Decision Emergence -A General Perspectiveand Some Sclective Illustrations-

pn Rnx c~n~ ~~ ~nnn i F Ttl Rl 1Rr THF NETHERLAND:Biblíotheek K. U. Brabant

II Y YIW~ YY I~ INII INII II