Tilburg University

Ultimatum proposals

Güth, W.

Publication date:1997

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Citation for published version (APA):Güth, W. (1997). Ultimatum proposals: how do decisions emerge? (CentER Discussion Paper; Vol. 1997-40).CentER.

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pM ~r,trJ~~ Discussion

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Tilburg University

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Centerfor

Economic Research

No. 9740

ULTIMATUM PROPOSALS- HOW DO DECISIONS EMERGE? -

By Werner Guth

April 1997

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(~CZi~ ci'7~

ISSN 0924-7815

UltimatLUn Proposals~How Do Decisions Emerge`?

~~-el-ner Gutht

April 9, 199i

Abst.ract.

'I'lu~ l~~eisir~ idca of de~~ision emergence is to geuerati~ the prefered decision alter-uative iiiste.~~l oF asstuning it as exogeneously given like in ueo-clrussical econutnicsan~l ~;aiuE~ ilieory. Tl~e particular problem of ultimatu~n proposals ha5 been selectedin urdor to relc on e~pcrimental obsen.atiuns when sl~ieculating how choices emerge.Oiu~ a~proach disrinyuishes primary and secondary cu~icerns of ultimatum proposersan~l illn5trate, ho~e qualiYative learning can (re)aliape p:eferenres over choices.

'Prelimiuar~~ i~lras n( tl~is suida wcre presented at 1 ZIF'-~VorksLop, L~uivrrtiity of Bielcfeld, iu Au;;ust14)94. I thank iLe pnrticip~nts, erpecially Reinliarrl Selte~i, f'ur an iuspiriug discussion as well a.5 SteHen

Hurk :uul ]~;ri~~ ~~~u Dauune for helpfiil commrnte.rHwulu,~ilt.[ uivei:tiih~ oE Berliu, Departmeirt uf Economics, Inst.itute for Economic Theory III, Span-

rl~~uer Str. 1. D- 10178 [3erlin, Genuauy

1 Introduction

In game tóc~ur,y and. mure generall~-, in neo-classical economics one usually assumes ex-

ogenously hi~-cu preferences determining the decision behavior of the varions parties. Al-

thuugL it is l,ussihle to derive preferences endoge~nously (see, for instance, Giith and

I~liemt. 1')D.4. who rely un the indirect evulntionary approach), this cíetermines only rather

special prcferc~nces or choices, c~~.g. the cvulutiouarily atable ones.

Llnlike in uc~crc~lassical ccunomics preferences, and thiis the choices which they induce, are

not exugeuously given but have to be gc~~nerated by a dyiiamic reasoning process. Gtith

(1995 aaicl 1US17) outlines a general perspective how choices of bo~mdedly rational deci-

sion cuakei:~ c uuld c~merge. The genera] iclea~.v are a behavioral repertoire based on former

experiencc~s and thoir recommendations fur qiialitatively and even quantitatively similar

nituatiurL~ ~cs well zis various submodules hy which one can generate choices for quanti-

tatively similar ("Directional Lcarsung"), qualit.atively similar (`'Adaptation Procedure")

and completely new ("New Problem Solver" ) choice problems.

The weakncss of such u gencral approec~li is I hat it rests on maiiy hypotheses of which only

fcw can I,e suliport,ed hy the available empirical, mostly experimental evidence. To avoid

thi5 we cnucc~iitrate here ou a particular choice problem, namely the proposal making in

ultimatum bargaining. Here a positive monetary amount c has to be allocated among

the part,ic.~ X a,nd 1' in the following way: The proposer X first selects a proposal (~, y)

with c-~ y - r and 0 G y C c wivch thc~~ responder can accept or rejeet. If Y accepts, X

receives :r and Y the residual amount ~- c- x, otherwise both parties get nothing.

Wherea.5 iu ~rther choice problems it rnay already Tieed qcute an effort to know a11 t,he

available choices. this is qnite obvious in a typical ultirnat.um bargaining experiment

where thc~ hroposer X caai choose between all offers y with 0 c y G c to the responder Y.

Of coursa. e~ liroposer will nsually restrict his attcntion to a few snch offers y e.g. to the

ec~ua] split r~ - r~2, ;y - e~3 and a very small value y.

We íiist ,tudy the structure of the reasoiring process b,y which au inexperienced proposer

X will elerivc~ hi~ c~hoice y where we distinguish primary (Section 2) and secondary (Section

1

3) concerns. Afterwards (Section 4) it wi11 be discussed how qualitative learrring (see, for

instance, 5elten and Buchta, 1994) chie to repeated play can change preferences over

propos~ds ~uid ther~.~by proposal tnaking. In the terminology of Guth (1997) we thus first.

concentrati~ nn decision emergence without qualitatively similar former experiences (the

"New Prubl~~iu Solver"-submodule) and then fucus on the other extreme case where one

can rely on former experiences due to playing the sarne game repeatedly (the `'Directional

Leanung'~-submodulc).

In om~ cuuclusiorL~; we discuss t.he general problem of decision emergence in the light of our

results which cuver only a very specific choice problem, but are based on empirical obser-

vations ancl therefore less speculative. It will take a long time and require many scholars

before having more general and ernpirically validated results. For this long joruney we

recormnencl to rely - as in our study - on etnpirical (field or experimental) observatiorLs

when trying tu develop theorics how decisions emerge.

2 Primary concernsof inexperienced proposers

It may appear conta~adictary that one ztissumes basic desires, e.g. for scarce resoruces like

inone,y, when explaining how preferences for certain choices are generated. Other studies,

rnost likely evolutionary ones (see, for instance, Guth and HIiemt, 1994) might try tu

justify b~rsic desires or primary concerns. Here it. is sitnply assumed fur the case at hand

that proposers prhnarily care for their monetary gains.

X Y

Ultimahun -~ Will y beProposal(x,y) accepted?

Result

X receives xyes ~ (Y receives y)

no~ X receives 0

(Y receives 0)

Figure 1: The sequential decision process of ultimatum bargaining

Z

Consider an individual who is asked to play the pazt of the proposer X in an ultimatum

garne and wL~~ envisages such an experiment for the first time. Although most persons will

have eapi~ricnc.ed tiltimatutn proposals before, the,y hardly seem to be able to traiLtilate

their pri~~ i~,us ,.tperiences to the alastract situation of the ultimatum game. Since the

monetai;v gaiu of íiroposer X depends on both (as illustrated by Figure 1), the demand and

the aa~eptan~~e decisiou, an inexperienced proposer X has T.wo major primary concerns.

uamcly t,is d~~,uand r- c- y and the "certainty" that his demand will be accepted-

Being a~cnre c,f tlicso two primary concerns the immediata task is to find out whether they

are corrrplimentary or conflicting. Such an ínvestigation requires a cognitive model of

the resp~,nder 1"a reaction behavior to the offers y rmder consideration. When generating

a prcrfar~~n~~e for uue nf the offers ~ rmder consideration, an inexperienced proposer X

ther~~for~~ L~is t,i iui~,t;inc how a- typical responder Y will react.

Note that thiti does not mean that proposer Y hïnrself would react in such a way. The

data of the so-called consistency tests where the same participant plays two ultimatum

garnes in different roles (Giith, Schrnittberger and Schwarze, 1982) clearly indicate that

some participants do not expect others to behave as they do. 1~4ore specifically, 5 of 37

participants were inconsistent in the sense that their detnand x and their acceptance

threshold r~ - in the sense that only offers ,y ) y would be accepted - add up to more

than to c an~l 17 in the sense of .r ~ y ~ c.

An obvi~nis idea to predict rc~ponse behavior in ultirnatum games is to assume that

most responders view the situation as basically symmetric since both parties (X and Y)

are needc~d for a,n agreement. The basic symmetry is, for instance, refíected by the

characteristic function ~i~ of the ultimatum game for which ~i ({X }) - v({Y}) - 0

a.nd ~, ({ ~, Y})- c. This implies a natura] aspiration level y- c~l of proposer Y. In

terrr~s of the two primary concerns t,his means that the equal split offer y- c~2 will be

surely accopted (what is always true in normal ultimatmn games, but not necessarily in

ultimatmn tiuhi;ames, see Giith and Tietz, 1989, Table 1).

3

Y

X

. v

Figure 2: How X expects Y to rexct

If respnnders expect y- c~2, tdl less favourable offers y with z~ G c~2 coc.ild trigger

unfricndly cinotions of responders and therefore he rejectecí ( see t.iie ~'aphical illustration

by Figiu'c~ 2). The likely resuh of ímaginiug response behaviour is therefore:

Prediction: All offers y c r.~2 will be less certaiiily accepted than the equal split y- c~2

whicli will be sureiy accepted.

For the t,wo primasy concerns of inexperienced proposers this, of conrse, means that these

concertL, are partly couHicting. The prediction seeins to explain why many inexperienced

decision wnkers shy away froin any risk of rejection t~y offeriug the equal split (in t.he study

of Giith ~wd Huck, 1994, for instance , 16 of 22 proposers X allocat.ing a cake of DM 16;

suggested an equal split b,y offering y- Db1 ti,-). Apparently the proposers resolved the

conHict hetween the two primary concerus by giving priority to t.he "certainty of having

one's offer accepted". in view of the psychological theory of cognitive dissonance

(Fest.inger. 1957) this caar be explained as a reevaluatiou of primary concerns ("it is

much iuc,re irnportant to gu~trantee acceptance than trying to achieve more" ) or as a

reinterpretation of facts ("iu spite of its sequential decision proeess the game is basically

ayumictric ~ ).

Of couise. uut z~ll inexperienced proposeis X avoid t.he "less certain" offers y C c~2. A

wurc auihitiocLti proposer X probably irnagines that a. respouder Y will grudgingly accept

an offer i~ ~ r~3 provided th~i~t the cost of choosing confíict are prohibitively high. An idea

4

for imagiuing Y's response behaviour for offers y G c~2 could be to predict Y's acceptance

threshold r~ with 0 G y G c~2 in the sense that X expects only offers y~ y to be accepted.

In our vic~w, aucL an acceptance threshold is a rather extreme form of irnagining response

behaviour. A more realistic pict.ure how proposer imagine response behaviour is graphi-

cally ilhistr~ited in Figure 3.

c0 s t 2

- - - 1acceptance rejectionis unlikely is unlikely

Figure 3: Irnagined responses to "low" offers y G c~2

Here the raugc of offers 0 G y G c~2 is partitioned into tlrree subregions, na.mely a

subinterval 0 G y c s of offers ,y with s) 0 which one views as highly risk,y. In the

subregion t G y C c~2 of offers y with t 1 s proposer X views the cost of choosing conflict

for Y as prnhihitively high, i.e. for X a rejection of such offers y is rather unlikely.

To have an easy notation we refer to t as an acceptance border and to s as a rejection

border. Whereas an acceptance threshold y assumes that these two borders coincide,

our hypothesis is that. s is usually smaller than t and that proposers X do not dare to

offer amoiuita y lower than t. The range of offers y with .s G y c t could be viewed as a

transition range from unlikely acceptance to unlikely rejection. We abstain frorn any

conjecture~s liow such a transition takes plaee. Since we focus on how proposers imagine

response behaviour, it is possible that also propasers do not form any definite expectations

either, when concerning offers y with s G y G t which they neither expect. to be likely

accepted nur to be likely rejected.

One worild uatura.ll,y expect that the acceptance border t increases less than proportion-

ally with the "cake size" c (experimental studies claiming "high stakes" are, for instance,

Carneroii. 1995, Hoffman, Mc Cabe, and Smith, in press, Slonirn and Roth, 1995) and

with Y's ~~nt itlement in the sense of Y's legitimate claims to participate in "eating the

5

cake c". Entitlement is Inost- convincingly introduced in reward and labotrr allocation

experimcnts (see. for instance, Shapiro, 1975) provided that both, the work effort and the

reward, are suffïciently high. Another way to provide entitlement is to auction experi-

mental positiorLS, e.g. the positions of X and Y in an ultimatum game (Guth and Tietz,

1986). Au ambiguous, but nevert.heless effective way of inducing entitlement has been

used by Hoffmann and Spitzer (1985).

Hypothesis: The acceptance border t with 0 G t G c~2 increases with the cake size c

less thau proportionally and also with the entitlement of responder Y.

That the acceptance border t should inerease less than proportionally with the cake size

c follows innnediately frorn the idea that. t represents the minimal cost wlvch certainly

prevents responder Y from choosing corrHict. If c becomes very la.rge, these costs shotild

increase less than proportionall,y since the rejection becomes more and more costly. Nlore

specifically, t should depend on c in a way int.ermediate to two boundary cases where t

doe.v not depend at- all on c acrd where t is proportional to c(see the bold curve in Figure

1).

t~t proportional to c

t-t(c)

t constant in c

t c

Figure 4: An ilhi5tration of how the acceptance border t should depend on the cake size c

Unfortuuately. the. data of usual ultimatum bargaining experiments do not reveal the

acceptance borrler t of responders Y since one only observes the actual response to X's

6

offer ,y o-iud uut the whole response stra,tegy. In experiments (see t.he survey of Giith and

Tietz, 19HcJ). which rely on the strategy rnethod, one cau observe the acceptance threshold

y hut in the~ titudies up to now neither calce size c nor Y's entitlement have been varied

systematir,clly. The value s of the rejection border cuuld be estimated as the highest va~lue

below wliic~li a high proportion, e.g. 95010, of all offers are rejected.

One rnight, uf course, rely on the chosen offer y as an incíicator of t.he acceptanee border t

whiclr a proposer X expects. Alt.hough the cake size c vv~ied a lot in many experimental

studies uf tbc riltimatwn game (see surveys of Giith ~id Tietz, 19i39, and Roth, 1995),

the amonnts c are naturall,y rather small (the highest arnount c seerns t.o be up to now ~

200). Within this limited range the first part. of t.tre fornrulated hypothesis could not be

confirmcd: The offered share y~c for the responder only weakly cíepends on c and does

not decrease sigruficantly with c as predicted.

Notice, however, that. most experímental studies of ultirnat.tun bargaining vary in strategi-

cally inessent.ial environmental aspects which ofteu oxert significant effects on the offered

share y~r. 'To test our hypothesis in a more rigorous way one shorrld perform an experi-

rnent which only varies c over some significant raarge.

3 5econdary concern ofinexperienced proposers

It has bcen elaborated above that a. proposer X has to employ some cognitive model of

response behavior in order to cor~struct his prefereuce for a certain ofíèr y urrder corrsid-

eration. In doing so hc t.ypically has to irnagine how a responder }' will feel when being

confrontc~d with a specific offer y and, especiallv, when beiug confronted with a"greedy

offer" y in t he serLSe of y bcing much smaller than c~2, i-e. far below the, natural aspiration

level 1~ - c~~2 of responders Y.

Y X

"low" r ~ .-~ ~

7

Figurc ~i: Tlce sequence of secondary concerns (in case of low oft'ers ~ proposer X

expe~c~ts Y to be vea,y upset what, in turn, upsets X)

hnagininh the situation of responder Y in such a way can change t-he proposer's concerns

consideral~ly. Irrespective of his primar,y coucern ~`Will my offer ,y be certainly accepted?"

he ma,y w~rut to avoid that Y can only grudgingly accept the offer y. In other words:

ImagininK the situation of responder Y' might provoke an empathy of proposer .X for

responder Y(see Figure 5 for an illustration). Such a proposer's concern for Y's well-

being is c nllE~d secondary since it often results from an investigation whether the proposer's

primary, couc.enis are cornpatible or conHicting.

One might uhject that a secondary concern of proposer X for Y's well-being is indistin-

guishable from X's fear that an offer y G c~2 will be rejected. This, however, is no longer

true whc~n one also consicíers the experimental results of related experiments. In the no

revenge: gnmes of Giith and Huck (forthcoming) res}~ionder f' can either only reject his

own payoff .y, but not the payoff a- of tlte proposer X, or Y has no veto power at all (see

the illustxntion by Figure 6). For the cake size c- DM 16,- the average offers were DM

5,82 aud DM 5,77, respectively. Although these amounts are significantly srnallPr t.han

the corresponcíing average offer of DM 7,86 in the ultinratum garne, they nevertheless

represent siguificant shares of the cake c- DM 16,-. This convincingly proves t.hat nrany

proposers .X develop a(secondary) concern for Y's well-being.

Will y beProposal(x,y) ~ ~cepted? ,'

X receives xyes ~ (1 receives Y)

no ~ X receives x(Y receives 0 or y)

Figm~c (i: ~l'he uo revenge-games (if Y receives y after "no", (s)he luts no veto power at

a,ll, otherwise Y can reject only y)

8

Another ~~:cy to experimentally test the strength of .Y's secondary concern for Y's well-

being is tu perfocm an experiment with three grvups of participants. One group of pro-

posers a~ aud responders Y play the usual ultimatum game with .X and }' deciding

simultauc,uusly about the oft'er y, respectively about the acceptance t}ueshold y. Another

grorrp of pruposers X' hrrs to make an offer ij which also must be accepted by a responder

Y whu. huwcwer, does not know that his choice of ,y decides whether ,y' is accepted and

who docs nut receive y' if it. is accepted. Thus X', knowing t.his, has no reason to be

concerned about Y"- Of course, also X should not be awa.re of X'.

One might object that in double blind-experiments of no revenge games one does not

observe sncli high avorage offers (sce Hoffman et al., 1994, and Bolton and Zwick, 1995).

In double Llind-experiments not only the partner Y, but also the experiment.er ca~nnot

observe tlie offér ,y of an individual proposer X. They guarantee this by allowing for

incornplc~te inforrnation in the sense t.ha.t at least for some pairs thc cake size is c- 0

where ouly the propo5er X lunrself, hut. neither the responder nor the experimenter knows

the true c:,rke size. Giith and Huck (fort.hcoming) also allow for a large (DM 323,-) and a

small cake (DIV1 16,-). Nevertheless 16 out of 42 proposers X with the large cake c- DM

38,- offercd more than the small cake (DM 16,-) in at least one of the two no revenge-

games, dc,tic~rihed ahove. Thus the pi~ssibility to "hide behind the small calce" alone cannot

prevent iuc~perienced proposers X to care for Y's well-being (the results of Hoffman et al,

1994, show a similar robustness when one introduces "double blindnPSS" ). We summarize,

what is illc~,5trated in I'igure 5, b,y

Conclusion: ~~1ien aualyzing whether or not a responder Y will accept an offer y in

the rauge 0 G y G c~2, many proposers X will develop a(secondary) concern for

Y's well-being what. inspires rnore generous offcrs y than those implied hy solely

considering .Y', primary concerns.

One has to ex~ect an eveu more important role of such secondary concerns for Y's well-

being whc~u the two parties X and Y interact face to face (one coiild describe such exper-

imerrts :rs O-blind ln~ocecíures). In a face to face-interaction most pexrple develop a gronp

feeliug wh~rt usually rulcs out unequal and therefore seemingly unjust. reward allocations

(see Frqy arrcí Bolmet, 1994).

q

4 Sliaping behavior by qualitative learning

If a propuser Plays the ultimatum game repeatedly against changing opponents, he usually

will impro~~c~ his behavior in the light of previous expericnces. As demor~strated above the

cogruti~'r c~nnsiderations of the proposer are rclated ruainlv to two qnestioits:

"How likely will an offer y c r.~2 be rejected"?"

and

'~Hot~ mnc li tiliould onc offer to Y anyhow'?"

Whereas the first question reflects the primary concern that X wants 6is offer to Y to

be accepted, the second question is rel:ited to the seconciary concern for Y's well-being

which sonte, bnt not necessarily all proposers will develop.

Qualit.a.tive or directíonal learning (see, for instance, Selten artd F3uchta, 1994) predicts

the direction of better decisions by inferenc~r~ti from previons experienc~s (see Figure 7 for

a graphical illustration).

I did "this", Next timebut "that" would ~ I choose "that"!have been better.

postdecisional reget ~ ` improved futurebehavior

Figtrre 7: The cognitive idea of directional learning ( or why looking back when rnoving

forward makes seuse)

VVhat onc cxn infer from previous results will, of course, depend on the specific experiences

~c.5 tvell a~ on one's cognitive ideas. Naturall,y a proposer X whose offer y G c~2 was

10

t-(t-1)Dyc - yc - yc-i 1-2 2-3 3-4 4-5 5-6 ~

accepted Dyc 1 0 5 0 5 1 1 12~c-~ Dyc - 0 8 10 10 17 14 59

~yt c 0 11 9 7 5 7 39re,jected ~y~ c 0 0 2 1 0 1 4

yf-1 ~y~ ~ 0 0 3 1 1 1 6

Tablc; 1:

rejected will conclude that he should be rnore generous next time. If an offer y) 0 is,

however. xccepted, one might regret to have offered so much. Thus qualitative ]earning

can be described for the case at. hand by the following rules:

Rule 1: A proposer X whose offer y c c~2 has been re,jected will increase it next time.

Rule 2: A proposer X whose oífer y 1 0 has been accepted will tend to decrease it or

keep it cunstant.

To test the two rules (1) and (2) we use the data of the experimental study by Giith

and van Damrne (1994). In their experiment a proposal consisted of three components

since a third part,y Z without strategic inHuence was included to combine the aspects

of ultirnatum t~arga,ining and dictatorship. Here only the data of those experiments are

used where responder Y knows y when deciding whether to accept. or not. In Table 1 we

only considcr those results where Y's information about the proposal was never varied

(Y either knows all three cornponents ar only the amount offered t.o him). The change

pyc - y~ - yc-i in the offer y to responder Y from period t- 1 to period t is classified

according to whether y~-1 has been accepted or rejected. If yt-1 has been accepted, only

~yt - 0 and ~y~ c 0 confirms rule (2), i.e. 98 of 110 observations. If yt-r has been

rejected, rule (1) predicts Dyc ~ 0 what is confirmed only in 6 of the 10 observations.

Thus we can conclude that rule (2) seems to be empirically valid whereas for rule (1) the

number of observations appears far too snrall for a final ,judgement.

In general, a proposer may not only hear about plays in which he took part actively,

but also rrbout other plays. A proposer X, whose thrifty offer y was luckily accepted,

may, for inst ance, nevertheless incre.ase his offer y to Y when he notices that even more

11

generous offers were rudely rejected. Similarly, a proposer who, e.g. out of his secondary

concern for Y's well-being, sees that he is the only one treating Y so well may rethink aaid

thereb,y give up his secondary concern for Y's well-being. More generally, it seems that

qualitative learning regarding the question how rnuch Y deserves will strongly depend on

experiences abont what others du. We just want to demonstrate that qualitative learning

can depend ou other experiences than the offers y. In the full information trials of

the experirnent by Giith and van Damme (1994) a responder did not only learn which

part y of the cake has been assigned to lum but also what X has granted to the third,

strategicall~~ iuessential party Z.

Here a propo,er X might have thought that responder Y will not only try to protect his

own share y, but also, e.g. out of a seeondary concern for party Z, the share z - c-~- y

of the third p~u~ty Z. Clearly, this would nrake it possible for X to soothe Y by granting

more to Z. There is, however, little support that Y cares for Z's well-being: Whenever

there was a rejection under full information it could be attributed to a low offer y c cj3,

i.e. responders Y did not sacrifice y simply because z was too low. Furthermore, proposers

X in avE~rage quickly have learned this and offered more to responders when the,y know z

in addition to ~, i.e. proposers X apparent,ly th~nght. it cheaper to bribe Y by increasing

y than to giant. more to Z when fearing that a too low a5signment z to Z might annoy

Y.

Notice that this sheds new light on proposer's secondary concerns for receivers as discussed

in section 3 above. Strong secondary concerns of X for Z's well-being should have induced

significant z-shares which were rarely observecL Of course, also responders Y could have

entertained such secondary concerns. A1 least in view of the results by Giith and van

Damme (1994) secondary concerns for receívers are rather utrreliable.

Although we could validate orily rule (2) of our hypothesis how qualitative learning

changes the preferences ofproposers who repea.tedly play the ultimatum game with chang-

ing opponents, the hypothesis, in general, seems intuitively convincing. Since reasonable

proposers ahy away from greedy offers, one usually (see Kagel, Kim and Moser, 1992, for

an exceptional study with a surprisingly high conflict quota) observes not enough conflicts

for testiug also rule (1). Studies with surprisingly krigh frequencies of confiict may rely

12

message forrn rn -(z, y, z) ~n. - ~round t- 3- round t 1-4 4-7 2-5 5-8

7l~-s ~~tr ~ 0 12(10) 7(5) 3(3) 4(2)accepted ~yc - 0 1.1 15 15 15

~yc G 0 9 1-1 16 17cIc-s ~yc ~- 0 0 ~ 1 0

rejected ~yc 1 0 1 0 1 0

Table 2: irc brackets the number of c~ses where nut ouly 2te. but also xc, has been increased

on procediu~es wluch migYrt shape the way in which directional learrung takes place. We

therefore refiain from applying rule ( 1) to other data sets with high conflict yuota. At

least for the data sets at hand the conch~sion t.hat the preferences of proposers are shaped

íiy qualitative learrung seems wcl]-founded and reasonable.

One may ask how behavior is shaped by experiences if the same iudividuals interact

repeatsdly. Usually eveu bormdecíly rational decision makers will see that a repeated game

(a base gaine is played repeatedly by the sanre persons) h~rs a completely different structure

than the (base) game itself. A proposer will therefore construct. preferences over offer

sequences rxther than only over his initial oífers ~ to responder Y where an offer sequence

rnust. not necessarily be complete ( one may not know how to cud a multi-period game

when starting it). This demonstrates tha~t decision emergence of ultimatum proposers

who repeatedly interact with t.he same responder is nearly as difficult as explaining the

choice behaviur in dyuanric games where at. le.~st partly previous moves are Icnown at later

decisions. We do not feel ready to challenge this far more difficult ttrsk.

Another difficulty results when a proposer is confrouted with maary experiences bet.ween

two successive trials. Instead of disctLSSing this abstractly without data we iliustrate this

again with the help of the data observed by Giith and van Damme (1994). As ment.ioned

before in their experiment a proposer X hací t.o allocat.e c arnong tkrree. persons X, Y and Z,

i. e. a proposal was a vect.or (.z, y, z) with xfzt~ z- r and x, rt, c 1 0(ihere was a smallest

positive money unit). In the experirnental trial, called cycle mode, a proposer played

altogethcr'J games successively agairLSt changing opponents which can be subdivided into

tlu~ee cycles. Here a cycle rneans that thc knowledge of Y about the proposal (x, y, z) was

varied systematically. Under full information 1' knew thc whole proposal (~, ~, z), under

essential information only p~, and uncíer irrelevant information only the component

l3

[tuiw~l

Infon uationruudit i~ iu

1~', y, z

3:r, r~, z

J El

y7

a, ~, zJ

'I'al~le ;i: 7~lii~ infurination cuuditions of t he cycli~ inode (Giith and van Dannne, 1994)

~ uf thE~ },r~~~~~~~:~1 (.~. y. ~). Li a ~.~i~lF~ ouc first plays the fnll, tlien the essential, and finally

11i~~ irrel~~~~aut iiif~n~inr~tion cun~lition.

Accordint; tu Table `L of the altogether 3G plays of the cycle mode only one began with

~~onHict iu tln~ first round (the E'iill inforiuation of the lst cycle). In accordance with

pr~~dictioii ( li nle 1) t his proposer reacte~~l }~y a niuch generous offer y to Y when he played

tlii~ full iiiliiruiation at;ain. Uf the 35 proposers whose first proposals were accepted 9

~Ic~crease~l. l.t kept.. :uid 12 increased their offe~rs to Y whei~ playing the full information

condition a~t;~~iii. This illustrates that rule (2) is leztis reliable when other experiences

iutervene. Ohviously most of the 12 proposers lcarned between thc first two plays of the

fiill infonnatiuu g~une, i.e. by experiencing the essential ~wid the irrelevant information

gatue, tli~it tl~ey have been too generous to Z and t.hat, to be sure of Y's ac~ceptance,

also respun~l~~r Y sl~oiild prolit frorn trcating Z less favoiirably (in 10 of the 12 cases ~c

iucreaseil tot;ether with y, twice :r wris kept constririt).

All '36 pru}~osr~ls of tlie second time of playing the full information game (the 4th round

altogether) wese accepted. Of these 36 proposers 14 decreased, 15 kept, and 7 increased

tlieir offer i~ to respou~ler }' so that the predictive succcss of rule (2) increased from

23~35 tii `1J~3(i. Of the 7 allucators, who incret~sed ~~ althoitgh thcir previous offer y was

accepted, b iucreascd .c together with i~. Thus the weaker support for rule (2) can be

inost.ly ~~~~ilaiurrl I,y attempts to "exploit," Z an~l to "bribe" Y by a larger offer y.

As reve~il~~~l fiv Table 2 the resiilts for the essential inessage ~n - i~ are not dramatically

ditferent. A~~tua.lly khe,y are slightly more in line with rule (2) t.han the corresponding

n;tinlts fur t li~~ fnll ~n~~.sagc furui m-(~~, y, z).

14

5 Conclusions

It, is an old anecdote (see Figirre 8) that a choice maker when being confronted with a.

difficult decision task will react rather angrily ("Are you kidding? This is serio~~s!" ) when

being helped by the "aclviee": "Wlry don't you simply ma3cirnize your utility!" What t.his

anecdote illustrates is that we aa-e not established with complete preferences telling us

what is best. The major problem of decision making is rather to construct. a preference

for a certain choice alternative what may sometimes be easy and sometinres dií~icult. The

easy choice problems are those where there is no conflict between (primary) concerrts, i.e.

there is nu uc~ed to reevaluate concerrts or ueglect discomforting evidence.

Y~c

0

x: wnat are me c,uvesi aoa ~ ~epte~r~ga

Answer. All points (x,y)on the seme am~earc equally goodTtey ere called"indifference curves"

X: Who is uidi8'ercot9Answer: Supposedly, you.X: Are you lódding7

lhis is serious!

1[

x

Figure ii: The old anecdote illustrating wh,y normative decision theory is of no help

Here we have concentrated on a particular and more difficult decision task, namely the

proposal making in iiltimatum bargaining where the two primary concerns "the own

demand a" aud "the certainty of having one's offer accepted' are couHicting. Flrrthennore,

the situatioit is a strategic one: More specifically, a proposer X has to predict how likely

it. is that a, certain proposal will be accepted by responder Y. Thinking about others in

such a way may inspire sorne concern for Y's well-being. We have narned this a secondary

concern tiiuce it. typically develops when analyzing whether the primary concerns are

conflictíng or not.

1J

The advant:rgE~ of concentrating on this particular choice problem is that most of our

hypotheses cuuld be b~~sed on experimental observations. We did not have to speculate

without fn~ ts, ~is it is partly true for Giith (1997). In particular, when demonstrating how

experiencr, (re)shape preferences for certain choices wP could rely on a rather rich data

set coulirniint; our prcrlictiu~LS.

The fact tL,it, espeeially in caae of couHicting concerns, t.he preferenee for a certain choice

alternativa has to be generated b,y a.n often cumbersome process of cogrutive mode~lling,

reevaluatiug eouccrrLS, re~interpretirrg evidence etc. makE~ it clear that preferences will

hardly ever be complete. On the contrary, one usually will start out to single out a few

relevant- ~lo~~ision alternativos when being offered too many as in the usual ult,inratum

game. How this is done, in general, hrrs not been discrossed here at all. In ultimatum

bargainint; most proposers seem to compare the equal split offer i~ - c~2 with some

nrore or Icss unfavorable offer y G c~2 for responde,r Y where prominence theory (see,

for instani~c, Albers and Albers, 19~3) undcubtedly has a lot to sa.y which offers y G c~2

easily coiuc to one's mind.

In our view, the theor,y of decision emergence is still iu a very preliminary state although

psychologi~ al lheorie.~a like cognitive dissonanee theory eertainly provide some guidance.

Since there are far t.oo rnany choice problems, theoretical results for particular decision

t.asks will uot sufíice. Our hope is therefore that certain aspects of the process, how

ultimatnm proposers generate their choices, are of gcsneral importance, e.g. how the

analysis uf primary concerrrs can generate secondary concerns and how qualitative learning

can (re)nh~ipe preferences (a more general attempt is Giith, 1997).

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18

No. Author(s)

9661 U. Gneen~ and J. Potters

9662 H.1. Biercns

9663 J.P.C. Blanc

9G64 M.].Lec

9665 C. Fernández, J. Osiewalskiand M.F.1. Stecl

9666 X. Han and H. Webers

9667 R. Kollmann

9668 R.C.H. Chene andJ.P.C. Kleijnen

9669 E. van Heck andP.M.A. Ribbers

9670 F Y. Kumah

9671 J.Jansen

9672 Y.H. Farzin, K.J.M. Huismanand P.M. Kort

9673 J.R. Magnus andF.J.G.M. Klaassen

9674 J.Fidrmuc

9675 M. Das and A. van Soest

9676 A.M. L,cjour andH.A.A. Verbon

9677 B. van Aarle andS.-E. Hougaard lensen

9678 Th.E. Nijman, F.A. de Roonand C.Veld

Title

An Experiment on Risk Taking and Evaluation Periods

Nonparametric Nonlineaz Co-Trending Analysis, with anApplication to [nterest and Inflation in the U.S.

Optimization of Periodic Polling Systems with Non-Preemptive,Time-Limited Service

A Root-N Consistent Semiparametric Estimator for Fixed EffectBinary Response Panel Data

Robust Bayesian Interence on Scale Parameters

A Comment on Shaked and Sutton's Model of Vertical ProductDifferentiation

The Exchange Rate in a Dynamic-Optimizing Current AccountModel with Nominal Rigidities: A Quantitativc Investigation

lmproved Design nf Queueing Simulation Experiments withHighly Heteroscedastic Responses

Economíc Effec[s of Electronic Markets

The Effect of Monetary Policy on Exchange Rates: How to Solvethe Puzzles

On thc First Entrance Time DisVibution of the MIDI~ Qucue: aCombinatorial Approach

Optimal Timing of Technology Adoption

Testing Some Common Tennis Hypotheses: Four Years atWimblcdon

Political Sustainability of Economic Reforrns: Dynamics andAnalysis of Regional Economic Factors

A Panel Data Model for Subjective Information on HouseholdIncome Growth

Fiscal Policies and Endogenous Growth in [ntegrated CapitalMarkets

Outpul Stabilization in EMU: Is Therc a Case for an EFTS?

Pricing Term Structure Risk in Futures Markets

No. Author(s) Title

9679 M. Dufwcnberg and U. Gnee .ry Efficicncy~, Reciprocity, and Expectations in an ExperimentalGame

9680 P. Bolton andE.-L. von Thadden

9G81 T. ten Raa and P. Mohnen

9682 S. Hochgucrtel andvan Socst

9683 F.A. de Roon, Th.E. Nijmanand B.J.M. Werkcr

9684 F.Y. Kumah

9685 U.Gnccry and M- Das

9fi8tí B. von Stengel,A. van den Elzen andD. Talman

9687 S.Tijs and M. Kostcr

9688 S.C.W. Eijffinger,H.P. Huizinga andJ.J.G. Lemmen

9689 T. tcn Raa and E.N. Wolff

9690 J. Suijs

969I C. Seidl and S.Traub

9692 C. Scidl and S.Traub

9693 R.(`1.W.J. Beetsma andH.Jensen

9694 M. Voorneveld

9695 F.B.S.LP. Janssen andA.G. dc Kok

969G L. Ljungqvist and H. Uhlig

9697 A. Rustichini

Blocks, Liquidity, and Corporatc ConUol

The Location of Comparative Advanlages on the Basis ofFundamentals only

The Relation between Financial and Housing Wealth of Dutch A.Households

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

Common Stochastic Trends in the Current Account

Experimental Investigation of Perceived Risk in Fínite RandomWalk Processes

Tracing Equilíbria in Extensive Games by ComplementaryPivoting

General Aggregation of Demand and Cost Sharing Methods

Short-Term and Long-Term Govemment Debt andNonresident Interest Withholding Taxes

Outsourcing of Scrvices and the Productivity Recovcry in U.S.Manufacturing in the 1980s

A Nucleolus for Stochastic Cooperative Games

Rational Choice and the Relevance of [rrelevant Altematives

Testing Decision Rules for Multiattribute Decision Making

[nflation Targets and Contracts with Uneertain CentralBanl:er Preferences

Equilibria and Approximatc Equilibria in Infinite PotentialGames

A Two-Supplier Inventory Modcl

Catching up with the Keynesians

Dynamic Progamming Solution of Incentive ConstrainedProblems

No. Author(s)

969R G.Giirkan and A.Y. bzge

9699 H. Huizinga

96100 H. Huizinga

96101 H. Norde, F. Patrone andS. Tijs

96102 M. Berg, A. De Waegenaereand J. Wielhouwer

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

96104 H. Huizinga and S.B. Nielsen

96105 H. Degryse

96106 H. Huizinga and S.B. Nielsen

96107 T. Dieckrnann

96108 F. de Jong andM.W.M. Donders

96109 F. Vcrbovcn

96110 D. Granot, H. Hamersand S. Tijs

96111 P. Aghion, P. Bolton andS. Fries

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

961 13 R. van den Brink andP.H.M. Ruys

96114 F. Palomino

961 15 E. van Damme andS. Hurkens

96116 E.Canton

Title

Sample-Path Optímization of Buffer Allocations in a TandemQueue - 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 forOp[imization Problems

Optimal Tax Reduction by Depreciation: A Stochastic Model

Existcnce and Approximation of Robust Stationary Points onPoly~topes

The Coordination of Capital Income and Profit Taxation withCross-O~~nership of Firms

Thc Total Cost of Trading Belgian Shares: Brussels VersusLonden

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

The Evolution of Conventions with Endogenous Interactions

Intraday Lead-Lag Relationships Between the Futures-,Options and Stock Market

Brand Rivalry, Mazket Segmcntation, and the Pricing ofOptional Engine Power on Automobiles

Weakly Cyclic Graphs and Delivery Games

Financial Restructuring in Transition Economies

Non-linear Asset Valuation on Mazkets with Frictions

The Intemal Organization of the Finn and its ExternalEnvironment

Conflicting Trading Objectives and Market Efficiency

Endogenous Stackelberg Leadership

Business Cycles in a Two-Sector Model of Endogenous Growth

970i J.P.J.F. Scheepens Collusion and Hierarchy in Banl:ing

No. Author(s)

9702 H.G. Bloemen andE.G.F. Stancanelli

9703 P.1.J. Herings andV.J. Vannetelbosch

9704 F. de long, F.C. Drostand B.J.M. Werker

9705 C. Femández and M.F.J. Stecl

9706 M.A. Odijk, P.J. Zwaneveld,J.S. Hooghiemstra, L.G. Kroonand M. Salomon

Title

[ndividual Wealth, Reservation Wages and Transitions intoEmployment

Refinements of Rationalizability for Normal-Form Games

Exchange Rate Target Zones: A New Approach

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

Decision Support Systems Help Railned to Seazch for `Win-Win' Solutions in Railway Network Design

9707 G. Bekacrt, R.J. Hodrick and The Implications of First-Order Risk Aversion for AssetD.A. Marshall Market Risk Premiums

9708 C. Femández and M.F.1. Steel Multivariate Student-i Regression Models: Pitfal(s and Inference

9709 H. Huizinga and S.B. Nielsen Privatization, Public Investment, and Capital Income Taxation

9710 S. Eijffinger, E. Schaling and Central Bank Independence: a Sensitivity AnalysisM. Hoeberichts

971 I H. Uhlig Capital Income Taxation and the Sustainability of PermanentPrimary Deficits

9712 M. Dufwenberg and W. Giith Indirect Evolution Versus Strategic Delegation: A Comparisonof Two Approaches lo Explaining Economic Institutions

9713 H. Uhlig Long Term Debt and the Political Support for a Monetary Union

9714 E. Charlier, B. Melenberg and An Analysís of Housing Expenditure Using SemiparametricA. van Soest Modcls and Panel Data

9715 E. Charlier, B. Melenberg and An Analysis of Housing Expenditure Using SemiparametricA. van Soest Cross-Section Models

9716 J.P. Choi and S.-S. Yi Vertical Foreclosure with the Choice of Input Specifications

9717 J.P. Choi Patent Litigation as an InCortnation Transmission Mechanism

9718 H.Degryse and A. Irmen Attribute Dependence and the Provision of Quality

9719 A. Possajennikov An Analysis of a Simple Reinforcing Dynamics Learning toPlay an "Egalitarian" Equilibrium

9720 J.Janscn Regulating Complementary Input Supply: Cost Correlation andLimitcd Liability

9721 J. ter Horst and M. Verbeek Estimating Short-Run Persistence in Mutual Fund Performance

No. Author(s)

9722 G. Bekacrt and S.F. Gray

9723 M. Slikker andA. van den Nouweland

9724 T. ten Raa

9725 R. Euwals, B. Melenberg andA. van Soest

4726 C. Fershtman and U. Gnecry

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

9728 F.H. Page, Jr.

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

9730 S.C.W. Eijffingcr andWillem 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. Wald:er, R.H. Thalerand A. Tversky

9736 T. Offcrman and J. Sonnemans

9737 R. Kabir

9738 M. Das and B. Donkers

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

Title

Target Zones and Exchange Rates: An Empirical Investigation

A One-Stage Model of Link Formation and Payoff Division

Club Etïiciency and Lindahl Equilibrium

Testing the Predictive Value of Subjcctive Labow Supply Data

Strategic Delegation: An Experiment

Campaign Expenditwes, Contributions and DirectEndorsements: The Strategic Use of Information and Money toIniluence Voter Behacior

Existence of Optimal Auctions in General Em~ironments

Optimal Budget Balancing Income Tax Mechanisms and theProvision of Public Goods

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

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

A Model of Random Matching and Price Formation

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

The Consistencw Principle for Set-valued Solutions and aNew Direction for the Theory of Equilibrium Refinements

Probabilistic Inswance

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

New Evidence on Price and Volatility Effects of Stock OptionIntroductions

How Certain are Dutch Households about Futwe lncome? AnEmpirical Analysis

Mandatory Pensions and Personal Savings in the Netherlands

9740 W. Guth Ultimatum Proposals - How Do Decisions Emerge? -

P - ëa,~::K~ën~.Ï.... ,~~onI ~ ~ I~ 11R1111~11 1 11 1 1