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Tilburg University
Boundedly rational decision emergence
Güth, W.
Publication date:1997
Link to publication in Tilburg University Research Portal
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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NR.48 1OII11C RCSeárCll a ermiiuiuuiiuim ii i i iiu iu ui i i iM iui~ iii
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