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Individual and Group Behavior in the Ultimatum Game: Are Groups More “Rational” Players?


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This article reports two experiments that compared the standard ultimatum game played by individuals with the same game played by three-person groups. In the group treatment, the members of the allocating group conducted a brief, face-to-face discussion in order to decide, as a group, on a proposed division, whereas the members of recipient group held a discussion on whether to accept or reject the proposal. If the proposal was accepted, each group member received an equal share of his group's payoff (the pie in the group condition was three times that in the individual condition). In both experiments, groups offered less than individuals. But as indicated by the low rejection rate in both treatments, groups were also willing to accept less. Copyright Economic Science Association 1998
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Experimental Economics KL581-05-Bronstein April 25, 1998 13:12
Experimental Economics, 1:101–108 (1998)
° 1998 Economic Science Association
Individual and Group Behavior in the Ultimatum Game:
Are Groups More “Rational” Players?
The Center for the Study of Rationality and Interactive Decisiion Theory and the Department of Psychology, The
Hebrew University of Jerusalem
This article reports two experiments that compared the standard ultimatum game played by individuals with the
same game playedby three-person groups. In the group treatment, the members of theallocating group conducted
a brief, face-to-face discussion in order to decide, as a group, on a proposed division, whereas the members of
recipient group held a discussion on whether to accept or reject the proposal. If the proposal was accepted, each
group member received an equal share of his group’s payoff (the pie in the group condition was three times that in
the individual condition). In both experiments, groups offered less than individuals. But as indicated by the low
rejection rate in both treatments, groups were also willing to accept less.
Keywords: ultimatum game, group decision
JEL Classification: C78, C92
and player 2 (the recipient). The two players are allocated a sum of money, and player 1
has to propose a division of this sum between himself and player 2. If player 2 accepts the
proposed division both are paid accordingly, if player 2 rejects the proposal both are paid
nothing. The game-theoretic prediction for this game is straightforward. If both players are
rational in the sense that each is concerned only with maximizing his own profit, player 1
should propose to keep all but a penny for himself and give a penny to player 2. Player 2
should accept this proposal since even a penny is better than nothing.
However, results from numerous experiments have shown that people do not behave in
line with thisprediction. Instead, offerstypically averageabout 40 to 50 percent of the total,
with the 50-50 split being the modal offer. Moreover, a substantial proportion of positive
offers are rejected. These findings have been replicated across different populations of
subjects using different amounts of money and different experimental procedures. And as
results “are no longer in question” (see also a recent review by Roth, 1995).
Individual versus group decisions
The experimental research on the ultimatum game has focused primarily on individual
behavior. Little systematic work has been done to study how groups behave in this game.
Experimental Economics KL581-05-Bronstein April 25, 1998 13:12
We see two reasons for studying group behavior. First, as pointed out by Messick et al.
(1997), in many real-life bargaining situations the negotiators are groups (such as families,
boards of directors, legislatures or committees) rather than individuals. Second, as we hope
to demonstrate, studying groups may shed new light on how individual subjects interpret
the ultimatum game and how they approach its solution.
This article reports two experiments which compared the ultimatum game played by
individualswith the same game played by three-persongroups. In the individual treatment,
player 1 had to propose a division of x points between himself and player 2, and player 2
had to decide whether to accept or reject the proposal. In the group treatment, the members
of the group in the role of player 1 had a few minutes of face-to-face discussion to propose
a division of the x points between their group and group 2, and the members of group 2
had a similar discussion to decide whether to accept or reject the proposal. If the proposal
was accepted, each player received an equal share of his group’s payoff (each point in the
group condition was worth three times that in the individual condition).
Since the strategic structure of the ultimatum game is not affected by this manipulation,
the game-theoretic solution for the two treatments is identical—namely, player 1, whether
an individual or a group, should propose to keep all but a single point and player 2 should
accept this proposal. Of course, we already know that individualsdo not behavein this way,
and the question that we focus on here is whether the behavior of groups is any different
from that of individuals.
There are several grounds for expecting groups and individuals to behave differently.
One possibility, which arises from social psychological research, is that groups are more
competitive or aggressive than individuals. The tendency of intergroup behaviorto be more
contentiousthaninterpersonalbehavior, termedthe“discontinuityeffect”,hasbeendemons-
trated in the two-person prisoner’s dilemma game (Insko and Schopler, 1987; Schopler and
Insko,1992). Totheextentthat this phenomenon generalizes to the contextoftheultimatum
game, groups would be more inclined to take advantage of their player 1 position and try
to obtain more for themselves than might be considered fair. However, if competitiveness
is a property of groups, then groups in the role of player 2 would share it and would be less
inclined to accept unfairoffersthan the less competitive individualplayers (Roth, 1995). So
under the “group competitiveness” hypothesis, one would expect lower offers and higher
rates of rejections in the group as compared with the individual condition.
Another possibility is that groups are more rational than individuals in the sense that they
offerless butare also willing toaccept less. This possibilityis based on the assumptions that
some individual subjects do not immediately grasp the strategic structure of the ultimatum
game and that group deliberation might serve to explicate the task. While some researchers
maintain that the ultimatum game is so simple that misunderstanding of the task is not a
real problem (Camerer and Thaler, 1995), Binmore et al. (1985) argued otherwise. In their
view, subjects, faced with a new problem, simply choose the equal division as an obvious
solution. However, “such considerations are easily displaced by calculations of strategic
advantage, once players fully appreciate the structure of the game” (p. 1180).
Can one expect group members to have a better understanding of the game’s strategic
structure following discussion and, consequently, to behave in a way that is more consis-
tent with the game-theoretic prediction? A recent review of the group-decision literature
Experimental Economics KL581-05-Bronstein April 25, 1998 13:12
(Kerr et al., 1996) demonstrates that group discussion can attenuate, amplify, or simply
reproduce the judgmental bias of individuals. The relative quality of group performance
depends primarily on the degree to which the normative principle pertaining to the decision
task is “demonstrably” correct. That is, the degree to which this principle, once voiced,
is accepted by group members as valid. In highly demonstrable tasks groups consistently
outperform individuals. This is because factions favoring the correct alternative are more
likely to prevail than comparable factions favoring an incorrect alternative (Davis, 1992).
shouldaccept any positiveoffersincesomething is betterthan nothing; therefore, we should
offer the bare minimum”) is self-evidently correct. However, we surmise that, if this is
indeed the case, groups would offer less than individuals; moreover, groups would be
willing to accept less. In other words, the “group rationality” hypothesis predicts that offers
in the group treatment would be lower than those in the individual treatment, whereas the
rejectionrates in thegroup treatment would not be anyhigher—thatis, rejection rateswould
be the same as or lower, than those in the individual treatment.
A third hypothesis concerning possible differences between groups and individuals in-
vokes the notion of a social norm. The social norm explanation of the ultimatum game
results maintains that subjects share a common perception of what constitutes a reasonable
offer under the circumstances (or develop such a notion during the course of the game).
Consequently, allocators make offers that they believe the recipients will find reasonable
and those are indeed accepted (Roth, 1995). This explanation received considerable sup-
port from a cross-cultural study by Roth et al. (1991), which compared the behavior in
the ultimatum game in the United States, Japan, Yugoslavia, and Israel. They found that,
while in all four countries the modal offers were in the typical range of 40 to 50 percent,
there were significant differences among the subject pools. For example, Israeli subjects
made lower offers than Americans. The important point is that Israeli subjects were also
willing to accept less and, as a result, that the rejection rate in Israel was not any higher
than that in the United States.
Social norms, however, are not known with certainty. Individual estimates of the norm
aremoreappropriately described as a randomdistributionaround some centralvalue(which
is presumably the social norm prevailing in the culture). Assuming that group members use
the opportunity for discussion to form a common notion of the social norm by averaging
their initial estimates, the distribution of group offers is the sampling distribution with
sample size 3 from the original individual distribution. This distribution has the samemean
as the original distribution but a smaller variance (more precisely, one-third).
If groups indeed have a more accurate notion of the prevailing norm, the probability of
rejections in the group treatment should be lower than in the individual treatment. Assume
thatthedistributionofreasonableoffersisidenticalforallparticipants, regardlessofwhether
they are in the allocator or the recipient role. Nonetheless, the samples of allocators and
recipients in a particular experiment, being two independent (and relatively small) draws
from that distribution, may hold different norms. The closer the means of these two random
samples, the smaller the expectedaverage gap between an allocator’s norm and a recipient’s
norm, and the lower the expected rejection rate. As argued above, the distribution of group
norms is narrower than that of individuals, and therefore two independent samples from the
Experimental Economics KL581-05-Bronstein April 25, 1998 13:12
group distribution are less likely to be different from each other than two samples from the
individual distribution. Thus, our third hypothesis implies that, on average, groups would
offer the same amount as individuals, but the rejection rate in the group condition would be
To summarize, we consider three possibilities: (1) groups are more competitive than
individuals, (2) groups are more “rational” than individuals, and (3) groups are more “nor-
mative” than individuals.
Experiment 1
Experimental procedure. Eighty male students participated in the experiment. Twenty
(ten pairs) were assigned to the individual condition and sixty to the group condition (ten
pairsofthree-persongroups). Inthe individualcondition, fourparticipantswererecruited at
a time, and each was shown individually into a separate room. Two of the participants were
given the allocator (player 1) instructions and two the recipients (player 2) instructions (see
the appendix). To ensure strict confidentiality, the participants were told that they would
be released one at a time (to minimize encounters in the corridors) and that they should not
expect to find out who they had played against.
Theamount to be dividedbetween an allocator anda recipient was 100 points, each worth
0.5 New Israeli Shekels (NIS 50 equaled approximately $17 at the time of the experiment).
Theallocatorswereaskedtowrite downtheirproposalastohowtodividethe100points(the
instructions are described in detail in the appendix). The experimenters then collected the
written offers from the allocators and transferred them to randomly preassigned recipients
in one of the other rooms for their decision. Each recipient had to indicate in writing
whether he accepted or rejected the offer. The participants received their payments in
sealed envelopes outside the test rooms.
In the group condition, twelve participants were recruited at a time. The participants
were randomly divided into four three-person groups, and each group was shown into a
separate room. Two of the groups were given the allocator (player 1) instructions and two
the recipients (player 2) instructions (see appendix). The members of the group in the role
of player 1 were told that they have up to ten minutes of free discussion to reach a joint
decision as to how to divide 100 points between their group and group 2. They were also
told that the members of group 2 would have a similar discussion to decide whether to
accept or reject their proposal. The participants in both groups were informed that, should
an offer be accepted, each group member would be paid NIS 0.5 for each point retained by
his group. Thus the group as a whole would receive NIS 1.5 per point and the total amount
to be divided between the two groups would be 150 shekels (approximately $51—three
times that in the individual condition). Except for the ten minutes time limit for reaching a
decision, there were no specificinstructions as to how the group’s decision shouldbe made.
Results. Table 1 shows the demands made by the ten individuals and the ten groups
(rejected demands are highlighted) and the mean demand in eachcondition. As can beseen
in the table, groups demanded an average of 60.8 percent of the total, whereas the average
individual demand was only 51.4 percent. These means are significantly different both by
Experimental Economics KL581-05-Bronstein April 25, 1998 13:12
Table 1. Distribution of demands (in percentage) in experiment 1 (rejected demands are highlighted).
Individuals 40 50 50 50 50 50 50 50 60 64 Mean=51.4
Groups 50 50 50 50 60 60 70 70 73 75 Mean=60.8
a t-test [t(18) = 2.56, p <.05] and by a nonparametric Mann-Whitney test [W = 80.5,
p <.05]. A single proposal (of 60: 40 ) was rejected in the group condition and none were
rejected in the individual condition.
Experiment 2
The purpose of experiment 2 was to test whether the pattern of results observed in experi-
ment 1 is robust and which aspects of it, if any, are sensitive to the experimental procedure.
Toward this end, we followed a double-blind procedure that allowed the participants a
greater degree of confidentiality. A similar procedure was used by Hoffman et al. (1994)
in the context of the dictator game. Hoffman et al. (1994) argued that, while in a typical
bargaining experiment subjects in the bargaining pairs do not know each other’s identities
and decisions, the experimenter is fully informed as to who made what decision. They
expressed the concern that subjects, being aware of this fact, might adapt their behavior in
an attempt to avoid a negative evaluation by the experimenter. Hoffman et al. (1994) in-
deed showed that in the dictator game a double-blind procedure, which guaranteed subjects
anonymity with respect to both the other subjects and the experimenter, led to considerably
less generous behavior.
Experimental procedure. Eighty male students participated in the experiment (as before,
twentywereassignedtotheindividualcondition, andsixty tothe groupcondition). Wegave
the allocators a total of fifty shekels in coupons (in denominations of 10, 5,and 1) and asked
them to indicate their allocation decision by dividing the fifty paper shekels and placing the
amount offered to the other side in a separate envelope to be delivered by the experimenter.
The allocators were asked to seal the envelope so that the experimenter who passed the
offers to the recipients could not know what they were. The recipients then delivered their
response in an envelope to the experimenter, who then passed it to the cashier (another
experimenter, who was stationed outside the lab and did not interact with the participants
during the experiment). The cashier paid each participant one real shekel for each paper
shekel in the envelope, and the participants were then released one at a time without an
opportunity to interact with one another. In the group condition, each group member was
paid one real shekel for each paper shekel retained by his group.
Results. Table 2 shows the demands made by the ten individuals and the ten groups (the
rejected demands are highlighted) and the mean demand in each condition. To facilitate
comparison with experiment 1, we present the demands on a percentage scale. As in
experiment 1, groups in the role of player 1 demanded more than individuals. The average
group demanded 66.6 percent of the total, whereas the average individual demanded 56.4
Experimental Economics KL581-05-Bronstein April 25, 1998 13:12
Table 2. Distribution of demands (in percentage) in experiment 2 (rejected demands are highlighted).
Individuals 46 50 50 50 50 50 60 60 68 80 Mean=56.4
Groups 50 50 60 60 60 70 76 80 80 80 Mean=66.6
percent. The differencebetween these two means is significant [t(18) = 2.00, p <.03,one
tail, and Mann-Whitney, W = 78.0, p <.05, one-sided test]. A single proposal (of 80-20)
was rejected in the individual condition and none were rejected in the group condition.
The double-blind procedure in experiment 2 had led to somewhat less generous offers.
Individualallocators demanded on average5 percent more than in experiment 1, and groups
demanded 5.8 percent more. To test whether these differences are statistically significant,
we performed an analysis of variance on the data combined from the two experiments with
experiment (or experimental procedure) as one factor and allocator type (groups versus
individual) as the other. The main effect of allocator type was, of course, statistically
significant [F(1, 36) = 10.1, p <.01], but the effect of the experimental procedure was
not [F(1, 36) = 3.57, p <.10].
Both experiments found that groups in the role of player 1 demanded more than individuals.
The mean difference between the group and the individual demands was in fact quite
large—about 10 percent of the pie. The distributions of demands (summed across the two
experiments) show that 60 percent of the individual allocators offered a 50-50 split, as
compared with only 30 percent of the groups. Demands of 60 percent or more were made
by 30 percent of the individuals as compared with 70 percent of the groups. Finally, only
a single individual demanded 70 percent or more of the pie, as compared with 45 percent
of the groups.
While groups were considerably less generous than individuals, the rate of refusals in
the two treatments was equally low (a single offer was rejected by a group in experiment 1
and a single offer was rejected by an individual in experiment 2). This implies that groups
not only offered less than individuals but were also willing to accept less. While we do not
have enough observations to warrant a definite conclusion, it is interesting to note that the
single proposal of 80-20 made in the individual treatment was rejected, whereas three such
proposals made in the group treatment were accepted.
This pattern of results supports the hypothesis that groups are more rational than indi-
viduals over the alternative hypotheses. Recall that if groups were more competitive than
individuals, lower offers in the group treatment should have been associated with higher
rejectionrates. Alternatively,ifgroups had a better perceptionofthe prevailingsocial norm,
the mean offer in the two treatments should have been the same.
As suggested earlier, one explanation for why groups offer less and are willing to accept
less is that groups have a better understanding of the game’s strategic structure and, in
particular, of the strategic advantage associated with the allocator’s position. The fact that
twoindividualallocators(oneineach experiment)offeredtogiveawaymorethan50percent
Experimental Economics KL581-05-Bronstein April 25, 1998 13:12
of the total, whereas none of the groups made such an unreasonable offer, is supportive of
this explanation. Further evidence will be obtained in future research by monitoring group
discussions. This will enable us to verify whether the strategic argument for making a low
offer is indeed voiced and, if it is, whether it has a decisive effect on the group’s decision.
A somewhat different explanation for the same pattern of results is that, when generating
their proposal, groups in the allocator role take into account the decision rule likely to be
used by the recipient group.
In particular, it is possible that group members operate under
the assumption that, for their proposal to be accepted, it needs only to be acceptable to the
majority of individuals in the other group, and therefore they can get away with lower offers
(although not as low as game-theoretic considerations prescribe). If this is indeed the case,
groups should offer more when the recipient is an individual player rather than a group.
This possibility also awaits further investigation.
The appendix to this paper is available upon request from the authors or through the home-
page of this journal
This research was supported by grants from the Israel Science Foundation (1994 to 1997)
and the Israel Foundation Trustees (1994 to 1996) to Gary Bornstein, and grants from the
Israel Science Foundation(1994 to 1997) and the Israel FoundationTrustees (1994 to 1996)
toIlan Yaniv. PleaseaddresscorrespondencetoGary Bornstein, Departmentof Psychology,
Hebrew University, Jerusalem 919905, Israel.
1. The single exception that we are aware of is a study by Messick et al. (1997). These researchers, however,
did not compare group behavior with individual behavior. Rather, they studied how individual allocators made
offersto a group of recipients. Themanipulationinvolved the decision rule by which the groupdecidedwhether
to accept the proposed division. In one condition, an offer was accepted if it equaled or exceeded the minimum
acceptable by each of the group members, while in the other condition, an offer was accepted if it equaled or
exceeded the minimumacceptable by anyof the members. Messick et al. found that individuals fail toaccount
for the group’s decision rule in making their allocations.
2. We chose to employ subjects of the same sex in an attempt to reduce potential “noise” associated both with
the subjects’ own sex and the groups’ sex composition. This consideration is particularly important given the
relatively small number of observations and the fact that sex differences in ultimatum game behavior were
reported in the past (Rapoport et al., 1994). We chose males simply because they were more easily available
at the time.
3. Bolton and Zwick (1995) also found that anonymity made little difference in the ultimatum game. In any
case, our purpose in conducting experiment 2 was establish the robustness of the individual-group difference
observed in experiment 1 rather than to examine the effect of anonymity per se.
4. Unless, of course, one speculates that there exists a different, less generous, norm for intergroup as compared
with interpersonal bargaining.
5. Although, as mentioned earlier, Messick et al. (1997) found that individuals fail to account for the group’s
decision rule in making their allocation decision, it is possible that groups are more capable of doing so.
Experimental Economics KL581-05-Bronstein April 25, 1998 13:12
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A growing body of research shows that people tend to act more antisocially in groups than alone. However, little is known about why having “partners in crime” has such an effect. We run an experiment using sender-receiver games in which we elicit subjects’ normative and empirical beliefs to shed light on potential driving factors of this phenomenon. We find that the involvement of an additional sender makes the antisocial actions of senders more normatively acceptable to all parties, including receivers. By contrast, empirical beliefs are unaffected by the additional sender, suggesting that antisocial behavior increases in groups because antisocial actions become more acceptable and not because acceptable behavior is expected less often. We identify a necessary condition for this effect: the additional sender has to actively participate in the decision-making.
Individuals are less likely to make morally desirable decisions when they are in groups. I study when this phenomenon makes groups less likely to produce a morally desirable outcome than one individual alone. I formulate and test a model in which a moral outcome occurs if at least one individual makes a costly decision. Using a lab experiment and data from field experiments on the bystander effect, I show that if most individuals are moral, the moral outcome is more likely to be produced by one individual, whereas if most individuals are immoral, it is more likely to be produced by a group. This rule is not only useful for reconciling previous mixed evidence on moral decision-making in groups, but may also be applied to better design organizations and institutions.
Moral judgments have a very prominent social nature, and in everyday life, they are continually shaped by discussions with others. Psychological investigations of these judgments, however, have rarely addressed the impact of social interactions. To examine the role of social interaction on moral judgments within small groups, we had groups of 4 to 5 participants judge moral dilemmas first individually and privately, then collectively and interactively, and finally individually a second time. We employed both real-life and sacrificial moral dilemmas in which the character's action or inaction violated a moral principle to benefit the greatest number of people. Participants decided if these utilitarian decisions were morally acceptable or not. In Experiment 1, we found that collective judgments in face-to-face interactions were more utilitarian than the statistical aggregate of their members compared to both first and second individual judgments. This observation supported the hypothesis that deliberation and consensus within a group transiently reduce the emotional burden of norm violation. In Experiment 2, we tested this hypothesis more directly: measuring participants' state anxiety in addition to their moral judgments before, during, and after online interactions, we found again that collectives were more utilitarian than those of individuals and that state anxiety level was reduced during and after social interaction. The utilitarian boost in collective moral judgments is probably due to the reduction of stress in the social setting.
Digital extortion has emerged as a significant threat to organizations that rely on information technologies for their operations. Using human subject experimentation, we study the effectiveness of message appeals in encouraging defenders to adopt two mitigation strategies, investment in security and refusal to pay ransoms, to digital extortion threats. We explore two types of appeals, benefit and normative, for this purpose. We find that the decisions of the defenders (representing any organization that can be a potential victim) deviate from the predictions of game theory. However, given the strategic interactions between the defenders and the attacker as well as noisy decision-making behaviors, it is challenging to untangle the influence of the appeals on the defenders. We develop a structural model based on the quantal response equilibrium framework to measure how message appeals change the defenders’ utilities of investment and payment refusal. Although the interventions may be successful in increasing the utilities of investment and/or payment refusal, their impacts on investment rate and payment rate are mitigated by the attacker reducing ransoms. Thus, it is challenging for an intervention to significantly boost a community’s investment rate or to suppress the ransom payment rate. We characterize how security outcomes of a community (including expected ransom, attack rate, investment rate, and payment rate) vary with the defenders’ utilities of investment and pay refusal. This paper was accepted by Chris Forman, information systems.
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The relative susceptibility of individuals and groups to systematic judgmental biases is considered. An overview of the relevant empirical literature reveals no clear or general pattern. However, a theoretical analysis employing J. H. Davis's (1973) social decision scheme (SDS) model reveals that the relative magnitude of individual and group bias depends upon several factors, including group size, initial individual judgment, the magnitude of bias among individuals, the type of bias, and most of all, the group-judgment process. It is concluded that there can be no simple answer to the question, "Which are more biased, individuals or groups?," but the SDS model offers a framework for specifying some of the conditions under which individuals are both more and less biased than groups. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
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Economics can be distinguished from other social sciences by the belief that most (all?) behavior can be explained by assuming that agents have stable, well-defined preferences and make rational choices consistent with those preferences in markets that (eventually) clear. An empirical result qualifies as an anomaly if it is difficult to "rationalize" or if implausible assumptions are necessary to explain it within the paradigm. This column will resume, after a long rest, the investigation of such anomalies.
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In an experiment comparing two-person bargaining and multiperson markets in Israel, Japan, the United States, and Yugoslavia, market outcomes converged to equilibrium everywhere, with no payoff-relevant differences between countries. Bargaining outcomes were everywhere different from equilibrium predictions (both in agreements and in the substantial frequency of disagreements) and differences were observed between countries. Because of the experimental design, the fact that the market behavior is the same in all countries supports the hypothesis that the observed differences are not due to differences in languages, currencies, or experimenters, but may tentatively be attributed to cultural differences. Copyright 1991 by American Economic Association.
In a series of experimental studies we have found that intergroup, compared to interindividual behavior, is more competitive and less cooperative (the discontinuity effect). After discussing the generality of this phenomenon, the possible mechanisms mediating the effect are analyzed. The role of fear and greed, in particular, are evaluated against existing empirical evidence. We also present a preliminary study using two n-person expansions of the Prisoner's Dilemma Game, which allow for competition within own-group as well as between groups. The chapter concludes with a consideration of possible ways of reducing discontinuity.
mere-categorization tradition / subjects into subsets / favoritism toward one's own category / perceived collectivity / entitativity / Tajfel assessment procedure / multiple alternative matrices cross-matrix inconsistency of responses / beyond categorization to competition / individual-group discontinuity / altruistic rationalization / social support for shared self-interest / group-schema (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Intuitions about aggregate behavior can be very compelling, and sometimes even persist in the face of contrary evidence. An example of apparent intuition-based assumptions about group decision-making behavior from each of the past four decades is discussed in detail: (a) Group superiority relative to individual performance—the fifties; (b) exaggerated group risk-taking relative to individuals—the sixties; (c) group size and performance level—the seventies; and (d) decision-making performance of free discussion groups and (implicit) procedural constraints—the eighties.
The demand game is a noncooperative two-person ultimatum game with one-sided uncertainty in which the Sender knows the value of the shared surplus (pie) but the Receiver only knows its probability distribution (Mitzkewitz and Nagel, 1993). We study experimentally the effects of systematic changes in the variability of the pie distribution on the Sender's proposals and Receiver's (binary) responses. In accordance with a behavioral theory that we propose, we find that 1.(i) the Sender's proportional share of the pie increases as the Receiver's uncertainty about the pie increases, and2.(ii) for a given pie distribution, the Sender's proportional share decreases as the actual pie size increases.