Understanding Social Preferences with Simple Tests
Author(s): Gary Charness and Matthew Rabin
Source: The Quarterly Journal of Economics, Vol. 117, No. 3 (Aug., 2002), pp. 817-869
Published by: Oxford University Press
Stable URL: https://www.jstor.org/stable/4132490
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UNDERSTANDING SOCIAL PREFERENCES
WITH SIMPLE TESTS*
GARY CHARNESS AND MATTHEW RABIN
Departures from self-interest in economic experiments have recently in
models of "social preferences." We design a range of simple experimenta
that test these theories more directly than existing experiments. Our expe
show that subjects are more concerned with increasing social welfare-sa
to increase the payoffs for all recipients, especially low-payoff recipie
with reducing differences in payoffs (as supposed in recent models). Sub
also motivated by reciprocity: they withdraw willingness to sacrifice to ac
fair outcome when others are themselves unwilling to sacrifice, and so
punish unfair behavior.
I. INTRODUCTION
Participants in experiments frequently choose actions
do not maximize their own monetary payoffs when those ac
affect others' payoffs. They sacrifice money in simple barg
environments to punish those who mistreat them and sh
money with other parties who have no say in allocations.
One hopes that the insights into the nature of nonself-in
ested behavior gleaned from experiments can eventually
plied to a variety of economic settings, such as consumer re
to price changes, attitudes toward different tax schem
employee response to changes in wages and employment
tices. To facilitate such applications, researchers have beg
develop formal models of social preferences that assume
are self-interested, but are also concerned about the payo
others. Different types of models have been formulated. "Di
* This paper is a revised version of the related working papers [Charn
Rabin 1999, 2000]. We thank Jordi Brandts, Antonio Cabrales, Colin Cam
Martin Dufwenberg, Ernst Fehr, Urs Fischbacher, Simon Gaichter, Edwa
ser, Brit Grosskopf, Ernan Haruvy, John Kagel, George Loewenstein, Ro
Nagel, Christina Shannon, Lise Vesterlund, an anonymous referee, and
participants at Harvard University, Stanford University Graduate School
ness, University of California at Berkeley, University of California at Sa
the June 1999 MacArthur Norms and Preferences Network meeting, th
Russell Sage Foundation Summer Institute in Behavioral Economics, the
2000 Public Choice meeting, the April 2000 Experimental Symposium at
nion, and the January 2001 ASSA meeting for helpful comments. We al
Davis Beekman, Christopher Carpenter, David Huffman, Christopher M
and Ellen Myerson for valuable research assistance, and Brit Grossk
Jonah Rockoff for helping to conduct the experimental sessions in Barcelo
financial support, Charness thanks the Spanish Ministry of Education
D101-7715) and the MacArthur Foundation, and Rabin thanks the Russe
Alfred P. Sloan, MacArthur, and National Science (Award 9709485) Foun
o 2002 by the President and Fellows of Harvard College and the Massachusetts In
Technology.
The Quarterly Journal of Economics, August 2002
817
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818 QUARTERLY JOURNAL OF ECONOMICS
ence-aversion models" assume that players are motivated to reduce
differences between theirs and others' payoffs; "social-welfare
models" assume that people like to increase social surplus,
caring especially about helping those (themselves or others) with
low payoffs; reciprocity models assume that the desire to raise or
lower others' payoffs depends on how fairly those others are
behaving.
In this paper we report findings from some simple experiments
that test existing theories more directly than the array of
games commonly studied. We then fit our evidence to a simple,
stylized model that encapsulates variants of existing models as
special cases, and formulate a more complicated new model to
capture patterns of behavior that previous models do not explain.
A major motivation for our research was a concern about
pervasive and fundamental confounds in the experimental games
that have inspired recent social-preferences models. Most notably,
papers presenting difference-aversion models have argued
that Pareto-damaging behavior-such as rejecting unfair offers
in ultimatum games, where subjects lower both their own and
others' payoffs-can be explained by an intrinsic preference to
minimize differences in payoffs. But this explanation is almost
universally confounded in two ways: first, opportunities for inequality-reducing
Pareto-damaging behavior arise in these
games solely when a clear motivation for retaliation is aroused.
Second, the only plausible Pareto-damaging behavior permitted
is to reduce inequality. Difference aversion has also been used to
explain helpful sacrifice-such as cooperation in prisoner's dilemmas-as
a taste for helping those with lower payoffs. But here
again two confounds are nearly universal: the games studied only
allow efficient helpful sacrifice that decreases inequality, and
only when a motive for retaliation is not aroused.
All of these confounds mean that the tight fit of these models
may merely reflect the fact that in many of the games studied
their predictions happen both to be the only way that subjects can
depart from self-interest, and to be the same as the predictions of
reciprocity.1
To provide a more discerning examination of social preferences,
our games offer an array of choices that directly test the
role of different social motivations, by testing a fuller range of
1. The analysis articulated in developing these models, on the other hand,
usefully demonstrates that the interpretations of authors (such as Rabin [1993]) that
helpful sacrifice is based on positive reciprocity are misleading-since such helpful
sacrifice is for the most part as strong when no positive feelings are aroused.
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UNDERSTANDING SOCIAL PREFERENCES 819
possible departures from self-interest, by eliminating confou
within games, and by inviting crisp, revealing comparisons a
games. Our data consist of 29 different games, with 467 p
pants making 1697 decisions.
In Section II we provide a simple linear, two-person mode
preferences that assumes that players' propensity to sacrific
another player is characterized by three parameters: the w
on the other's payoff when she is ahead, the weight when sh
behind, and the change in weight when the other player
misbehaved. This embeds difference aversion, social-welfare
erences, and other preferences as identically parsimoniou
tractable special cases of a more general model. By way o
shift parameter, it also embeds a simple form of reciproc
Section III we explain our experimental procedures and r
results. We interpret our results without invoking inten
based reciprocity in Section IV, and with reciprocity in Secti
We analyze our results both by comparing the percentage of
that different models explain, and with regression analysis o
best-fit parameter values of the model of Section II.
Our findings suggest that the role of inequality reduction
motivating subjects has been exaggerated. Few subjects sac
money to reduce inequality by lowering another subjects' pay
and only a minority do so even when this is free. Indeed
observed Pareto-damaging behavior more often when it incre
inequality than when it decreased inequality. While this comp
son is itself confounded by other explanations, our data stro
suggest that inequality reduction is not a good explanati
Pareto-damaging behavior.2 By contrast, difference-ave
models do provide an elegant insight into players' willingn
sacrifice when ahead of other players. Yet social-welfare pref
ences provide an even better theory of helpful sacrifice. By
iting far greater concern for those who are behind than those
are ahead, they also predict helpful sacrifice by those with h
payoffs. By positing a concern for efficiency, however,
welfare preferences predict that even if players are behind t
may sacrifice small amounts to help those ahead. Unlike d
ence aversion, therefore, social-welfare preferences can ex
the finding in our data that about half of subjects make ineq
2. Other recent papers similarly providing data that calls into questi
role of inequality reduction in Pareto-damaging behavior include Kagel an
[1999] and Engelmann and Strobel [2001].
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820 QUARTERLY JOURNAL OF ECONOMICS
ity-increasing sacrifices when these sacrifices are efficient and
inexpensive.3
To test the role of reciprocity, we study simple response
games where Player B's choice follows a move by Player A to forgo
an outside option, and compare B's behavior with his behavior
given the same binary choice where A either forwent a different
outside option or had no option at all. Our data replicate recent
experimental evidence that positive reciprocity is not a strong
force in experimental settings.4 But subjects exhibited a form of
reciprocity we call concern withdrawal: they withdraw their willingness
to sacrifice to allocate the fair share toward somebody
who himself is unwilling to sacrifice for the sake of fairness.
Subjects also significantly increased their Pareto-damaging behavior
following selfish actions by A.
Overall, straightforward interpretation of specific games and
summary descriptive statistics show that social-welfare preferences
explain our data better than does difference aversion, and
that subjects clearly behave reciprocally. Our regression analysis
indicates that a B who has a higher payoff than A puts great
weight on A's payoff. However, if B has a lower payoff than A and
no reciprocity is involved, the weight on A's payoff is close to 0.
When A has mistreated B, B significantly decreases positive
weight or puts negative weight on A's payoff.
While most of our data and our formal tests concern twoplayer
games, in Section VI we discuss results in the five threeplayer
games. These games provide some evidence for a multiperson
generalization of social-welfare preferences, and further
demonstrate the role of reciprocity by showing that subjects'
preference between two allocations is for the one where an unfair
first mover gets a lower payoff. We also demonstrate that subjects
are not indifferent to the distribution of material payoffs among
other people.
Our experiments add to other recent evidence in providing
raw data for developing better models of social preferences. Since
there are clearly many forces at work in subjects' behavior, researchers
are faced with the decision as to how complex a model
3. Andreoni and Miller [20001, Charness and Grosskopf [2001], and Kritkos
and Bolle [1999] find similar results, with significant numbers of participants
opting for inequality-increasing sacrifices to help others.
4. One exception we find to this pattern is that positive feelings reduce
difference aversion when self-interest is not at stake. We return to this finding in
our concluding discussion. We also note that McCabe, Rigdon, and Smith [2000]
find, in one simple game, significant and statistically significant evidence of
positive reciprocity.
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UNDERSTANDING SOCIAL PREFERENCES 821
to formulate, trading off progress on applicable models a
the quest for psychological and empirical accuracy. Our
perspective is that too much will be lost if experimentalists
too quickly to calibrating highly simplified models that
prevalent phenomena such as reciprocity. At this stage,
ought to be developed that help interpret psychologically
and empirically prevalent patterns of behavior common
broad array of games.
In this spirit, in Appendix 1 we develop a multiperson m
of reciprocal-fairness equilibrium that combines social-w
preferences and reciprocity. We presume that players are
vated to pursue social welfare, but withdraw the willing
give others their social-welfare shares when these others
being unfair, and may even sacrifice to punish them. Desp
complexity, this model clearly omits many factors that play
in laboratory behavior, and hence is unlikely to fit the
tightly. Rather, it is meant to provide incremental conceptu
calibrational progress in understanding the nature of so
preferences.
For those who instead feel it is more urgent to develop s
pler and more applicable models, our analysis in the body
paper shows that an equally parsimonious alternative m
explains behavior in our data better than difference-aver
models. The alternative essentially reverses the weight that
ers put on the payoffs of others doing better than them
strongly negative to weakly positive, reflecting a willing
pursue social efficiency when it comes at a small cost t
worst-off player.5
That said, we do not believe this paper establishes de
tively that previous interpretations of nonself-interested be
have been wrong.6 Rather, our analysis clarifies clear con
5. This means, of course, that the more parsimonious model that ass
players ignore the payoffs of others who are ahead of them performs
as difference-aversion models. We do not think our simple alternative will
a good fit for the broad set of games economists should care about. It o
does not explain rejections of unfair offers in ultimatum and bargainin
which is the primary source of difference-aversion models beginning with
[1991]. Our claim is merely that-once we start examining a broader a
games-it will provide a better fit than difference-aversion models. Dif
aversion models predict rejections in the ultimatum game. But they mak
predictions than pure self-interest in other games that are simpler, mo
nostic, and (we would contend) more economically relevant than the ult
game.
6. Indeed, while our analysis stresses that our data contradict differenceaversion
models, we do not think we have conclusively disproved these models.
This is for (at least) two reasons. First, some of the differences from earlier
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822 QUARTERLY JOURNAL OF ECONOMICS
in the previous research supporting those interpretations. More
than our specific findings and interpretations, in fact, we hope
that this paper helps move experimental research away from
studying the existing, manifestly misleading, menu of games and
toward a wider range of simpler and more diagnostic games. We
conclude in Section VII with a discussion of some of the issues
raised by this program and with some suggestions for new directions
of research.
II. SocIAL PREFERENCES
In this section we outline a simple conceptual model of social
preferences in two-person games that embeds different existing
theories of social preferences as different parameter ranges, and
allows for the estimation of these parameter values in our empirical
analysis below.' Letting ITA and TB be Player A's and B's
money payoffs, consider the following simple formulation of
Player B's preferences:
UB(TA,qTB) = (p r + ?r's + s0 q) ? -TA
+ (1 -p-r--'s-s-0q) 'rB,
where
r = 1 if 'rB > iTA, and r = 0 otherwise;
s = 1 if ITB < 7A, and s = 0 otherwise;
q = - 1 if A has misbehaved, and q = 0 otherwise.
This formulation says that B's utility is a weighted sum of
her own material payoff and A's payoff, where the weight B places
on A's payoff may depend on whether A is getting a higher or
research in both our design and in our results--especially the relative lack of
Pareto-damaging behavior-demand caution in extrapolating results from our
experiments. Second, it is clear that subject behavior is heterogeneous, and that
there are subjects who exhibit some degree of difference aversion in some circumstances.
Fehr and Schmidt [1999], for instance, have argued that only 40 percent
of subjects need be difference-averse to explain the phenomena they explain. This
is arguably consistent with our data. More generally, insofar as the existing
literature has emphasized the existence of difference aversion as a force among
some subjects, our evidence suggesting that it is weaker and rarer than very
opposite forces may not contradict what has been found so far.
7. By "conceptual," we mean that one major component of preferences-the
motive to punish unfair behavior-is left underspecified. The model in Appendix
1 develops the additional framework needed to fully formalize our assumptions
about reciprocity.
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UNDERSTANDING SOCIAL PREFERENCES 823
lower payoff than B and on whether A has behaved unfai
parameters p, u, and 0 capture various aspects of socia
ences. The parameter 0 provides a mechanism for modelin
procity, which we shall return to below. The parameters p
allow for a range of different "distributional preferenc
rely solely on the outcomes and not on any notion of reci
We begin by discussing purely distributional preferences,
may be appropriate either in contexts where reciprocity i
not to motivate subjects or when modelers are looking for
proxy for full-fledged preferences that include reciprocity
One form of distributional preferences (consistent w
psychology of status) is simple competitive preferences. T
be represented by assuming that a < p - 0, meaning th
B always prefers to do as well as possible in comparis
while also caring directly about her payoff. That is, pe
their payoffs to be high relative to others' payoffs.9 A mo
lent hypothesis about distributional preferences is wha
"difference aversion," and is exemplified by Loewenstei
man, and Thompson [1989], Bolton and Ockenfels [2000
Fehr and Schmidt [1999]. This approach is related to e
theory as classically formulated, as these models assum
people prefer to minimize disparities between their ow
tary payoffs and those of other people. Difference aversio
sponds to a < 0 < p < 1. That is, B likes money, and pre
payoffs are equal, including wishing to lower A's payoff w
does better than B. Fehr and Schmidt [1999] and Bolton and
Ockenfels [2000] show that difference aversion can match experimental
data in ultimatum games, public-goods games, and some
other games where many subjects sacrifice to prevent unequal
payoffs.
Yet there is considerable experimental evidence that does not
match these models. Andreoni and Miller [2002], for instance,
test a menu of simple dictator games where many subjects give
money to subjects already getting more money, which is the
opposite of difference aversion. Moreover, they interpret participants
who equalize payoffs to be pursuing (what we are calling)
social-welfare preferences rather than difference aversion. Our
8. Another way of writing this utility function that some readers might find
more intuitive is to break it down into two cases: when 'rB iTAr, UB(ITA, 'TB) =
(1 - p - Oq)Irr + (p + Oq)TA; when TrB - :ITA, UB(ITA, TB) (1 a- - Oq)rTB +
(o + Oq)rwA.
9. Assuming that a - p says that the preference for gains relative to the otherperson is at least as high when behind as when ahead.
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824 QUARTERLY JOURNAL OF ECONOMICS
notion of social-welfare preferences subsumes the different cases
examined by Andreoni and Miller [2002], by letting the parameters
take on the values 1 > p _ a > 0.10 Here, subjects alwaysprefer more for themselves and the other person, but are more in
favor of getting payoffs for themselves when they are behind than
when they are ahead.11 Social-welfare preferences are the twoplayer
case of the more general notion, related to the ideas presented
in Yaari and Bar Hillel [1984], that players want to help
all players, but are particularly keen to help the person who is
worst off.12
Since social-welfare preferences assume that people always
prefer Pareto improvements, they cannot explain Pareto-damaging
behavior such as rejections in the ultimatum game. Of course,
reciprocity is a natural alternative explanation for Pareto-damaging
behavior. Several models have assumed that players derive
utility from reciprocal behavior, and so are motivated to treat
those who are fair better than those who are not.13 Roughly put,
these models say that B's values for p and u vary with B's
perception of player A's intentions.
Any reciprocal model must embed assumptions about distributional
preferences. Rabin [1993] and Dufwenberg and Kichsteiger
[1998] concentrated on modeling the general principles of
reciprocity, and employed simplistic notions of fairness and distributional
preferences. Falk and Fischbacher [1998] combine
difference aversion and reciprocity into a model where a person is
less bothered by another's refusal to come out on the short end of
a split than by a refusal to share equally. Roughly put, they
assume that B has preferences u < 0 < p < 1 when they feel
neutral or positive toward another person, but that B's values for
p and a diminish if A's behavior suggests that A assigns the
10. It is also natural to impose a 1/2, which says that B is not moreconcerned about A's payoff than his own when A is getting a higher payoff. Note
that when p = V = 1/2, UB(,A, rTB) = (IA + rB)/2, so that B puts equal weight
on each player's material reward.
11. Earlier studies by Frohlich and Oppenheimer [1984, 1992] similarly find
that subjects reach agreements that tend to maximize total payoffs, while observing
an income floor for individuals in the group. They also find statistical relationships
between choices and partisan political preferences.
12. A fourth possibility (which could be labeled "equity aversion") that also
fits into our framework would be to assume that a person puts more weight on a
person when that person is ahead rather than behind.
13. Studies demonstrating reciprocity that cannot be explained by distributional
models include Kahneman, Knetsch, and Thaler [1986], Blount [1995],
Charness [1996], Offerman [1998], Brandts and Charness [1999], Andreoni,
Brown, and Vesterlund [1999], and Kagel and Wolfe [1999]. Other studies, such as
Bolton, Brandts, and Katok [2000] and Bolton, Brandts, and Ockenfels [1998],
yield more equivocal or negative evidence regarding reciprocity.
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UNDERSTANDING SOCIAL PREFERENCES 825
weight p - 0 to B's well-being. Importantly, Falk and Fischbac
assume that B does not resent harmful behavior by A if it se
to come only from A's unwillingness to come out behind r
than A's selfishness when ahead. That is, B retaliates against
behavior implying that A's p is too small, but not against behavior
indicating that a is small or negative. An alternative hypothesis
about reciprocal preferences follows naturally from social-welfare
preferences: people have preferences 1 - p > a > 0 when they feelpositive or neutral toward other players, but when these others
pursue self-interest at the expense of social-welfare preferences,
then they decrease these weights.
Reciprocity can be captured simply (and crudely) by assuming
that 0 > 0: when q = - 1, indicating that A has "misbehaved"
by violating the dictates of social-welfare preferences, this essentially
assumes that B lowers both p and a by amount 0. In
Appendix 1 we define the solution concept reciprocal-fairness
equilibrium, combining social-welfare motivations and intentions-based
reciprocity in a model of social-preferences in multiperson
games. But the remainder of the paper concentrates on
testing the simple model of this section. After explaining our
experiments and presenting our results in the next section, in
Section IV we discuss the fit of our data with different distributional
models by assuming that 0 = 0, and in Section V we explore
the role of reciprocity in our data by considering our model when
0 is not restricted.
III. EXPERIMENTAL PROCEDURES AND RESULTS
We report data from a series of experiments in which participants
made from two to eight choices, and knew that they would
be paid according to the outcome generated by one or two of their
choices, to be selected at random. A total of fourteen experimental
sessions were conducted at the Universitat Pompeu Fabra in
Barcelona, in October and November 1998, and at the University
of California at Berkeley, in February and March 1999. There
were 319 participants in the Barcelona sessions and 148 participants
in the Berkeley sessions. No one could attend more than
one session. Average earnings were around $9 in Barcelona and
$16 in Berkeley, about $6 and $11 net of the show-up fee paid. In
Barcelona, 100 units of lab money = 100 pesetas, equivalent to
about 70 cents at the contemporaneous exchange rate; in Berkeley,
100 units of lab money = $1. Experimental instructions are
provided in Appendix 2.
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826 QUARTERLY JOURNAL OF ECONOMICS
We conducted no pilot studies and report all data from experiments
conducted for this project that were played for financial
stakes.14 We designed the Berkeley games after examining
the Barcelona results, and modified several games after observing
earlier results.15
Students at Pompeu Fabra were recruited by posting notices
on campus; most participants were undergraduates majoring in
either economics or business. Recruiting at Berkeley was done
primarily through campus e-mail lists. Because an e-mail sent to
randomly selected people through the Colleges of Letters, Arts,
and Sciences provided most of our participants, the Berkeley
sessions included students from a broader range of academic
disciplines than is common in economics experiments.16
Games 5-12 in Barcelona were played in one room, while
comparison games were played in a simultaneous session in another
room. The groups in the separate rooms were randomly
drawn from the entire cohort of people who appeared. Parallel
sessions were impractical in Berkeley, but some effort was made
to run sessions at similar times of day and days of the week, to
make the subject pools in different treatments as comparable as
possible.
In all games, either one or two participants made decisions,
and decisions affected the allocation to either two or three play-
14. We also collected survey responses from Barcelona students about how
they would behave in hypothetical games, some of which suggested greater difference
aversion than for the games we ran for stakes, and hence to contradict our
results. Since the first draft of this paper was circulated, we have run additional
related experiments (for another paper) whose analysis we had not intended to
and do not include in this paper. Although these are heavily confounded with
reciprocity interpretations, we note that in these new data we observed a rise in
the percentage of responding subjects exhibiting difference-averse behavior in
three of the conditions we report on here. But by and large the new data seem to
qualitatively and quantitatively support the conclusions of this paper, and we do
not have data in our possession that we believe broadly contradicts any of our
interpretations in this paper.
15. Specifically, Barc4 was designed after the Barc3 results were observed
and was chosen to eliminate the possibility that B could believe that A's choice to
enter was motivated by an expectation of higher payoffs. In addition, after the
fourth Berkeley session we deleted two planned games: 1) A chooses (375,1000) or
gives B a (350,350) vs. (400,400) choice, and 2) A chooses (1000,0) or gives B a
(800,200) vs. (0,0) choice. We added two games: 1) A chooses (750,750) or gives B
a (800,200) vs. (0,0) choice, and 2) A chooses (450,900) or gives B a (400,400) vs.
(200,400) choice. With these exceptions, we designed the entire set of games in
Barcelona before conducting any experiments, and designed the entire set of
Berkeley experiments after we gathered results in Barcelona and before conducting
any experiments in Berkeley. We did not use the results of the survey games
for design purposes.
16. As a result of recruiting a smaller number of participants through an
advertisement in The Daily Californian, our pool of participants also included a
few colorful nonstudents.
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UNDERSTANDING SOCIAL PREFERENCES 827
ers. In two-player games, money was allocated to players
based either solely on a decision by B, or on decisions o
and B. In three-player games, money was allocated to p
B, and C, based either solely on a decision by C, or on dec
both A and C. Participants were divided into two groups s
opposite sides of a large room and were given instruc
decision sheets. The instructions were read aloud to th
Prior to decisions being made in each game, the outcome f
combination of choices was publicly described (on the blac
to the players.
In games where more than one player had choices,
were played sequentially. Player A decision sheets were co
then B decisions were made, and the sheets were collected
two cases, A decision sheets were collected, and then C
Following Bolton, Brandts, and Ockenfels [1998], Bo
Brandts, and Katok [2000], and Brandts and Charness
each game was played twice, and each participant's role
across the two plays. Participants were told before their f
that they would later be playing in the other role, but (to
age reputational motivations) were assured that pairin
changed in each period.
Except in the case of Games 1-4, participants played
than one game in a session. Games were always present
participants one at a time, and decision sheets were col
before the next game was revealed. In the sessions wit
5-12, each participant played two games. In the Berke
sions, each participant played four games. Participants kn
the payoffs in only some of the games would be paid,
mined by a public random process after all decisions we
One of two outcomes in Games 1-4, two of four in Gam
and two of eight in Games 13-32 were paid.
Some aspects of our experimental design may disc
comparing our results with those of other experiments. O
role reversal and multiple games in sessions may have g
different behavior than had each participant played just o
in one game. In addition, whereas many experiments h
ers make the same decision repeatedly, we had each pa
make each type of decision only once. Finally, to maxi
amount of data in response games, a responder (B or C
told before she made her own decision about the decisions of the
first mover (A). The responder instead designated a contingent
choice (the strategy method of elicitation), after being told that
her decision only affected the outcome if A opted to give the
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828 QUARTERLY JOURNAL OF ECONOMICS
responder the choice, so that he should consider his choice as if
A's decision made it relevant for material payoffs." We do not
believe that the use of either role reversal or the strategy method
is an important factor in our results.
Table I reports our results, organizing the games by their
strategic structure and the general nature of the trade-offs involved.
We label the twelve Barcelona treatments Barcl to
Barcl2, where the number indicates the chronological order
the game, and label the twenty Berkeley treatments as Berkl3
Berk32. In parentheses next to the game is the number of
ticipants in the session. The x in Barcl0 and Barcl2 signify t
C was not told her allocation before her choice, in a design mea
to discourage her from comparing A's and B's payoffs with
own.18
This array of games was chosen to provide a broad range
simple tests that have some power to differentiate among vario
social preferences. The seven dictator games isolate distrib
tional preferences from reciprocity concerns, and variously all
a responder to sacrifice to decrease inequality through Pare
damaging behavior, to sacrifice to increase inequality and t
surplus, and to affect inequality at no cost to himself. Th
provide a useful range upon which to test the value of p and
The twenty response games have an even wider range o
options by B and a wide range of options by A. There are ga
where entry by A hurts B and where entry helps B, and wh
this help or harm is or is not compatible with difference avers
or social-welfare preferences. We use these games as further te
of the distributional models by examining both B and A behavi
and can examine reciprocity by seeing how B's response depe
on the choice A has forgone. To aid inferences about reciprocit
we have many sets of games where B's choices are identical,
A's prior choice (or lack thereof) is varied.
In the next two sections we analyze our results to highlig
17. See Roth [1995, p. 323] for a hypothesis that this strategy method p
sibly induces different behavior than does a direct-response method in wh
players make decisions solely in response (when necessary) to other pla
decisions. Cason and Mui [1998] and Brandts and Charness [2000] conduct test
where it does not seem to matter much; Shafir and Tversky [1992] and Cr
[2000] find some difference in the propensity to cooperate in a prisoner's dilem
using the two methods.
18. We took pains to ensure that participants did not think that their beha
ior influenced x. Participants were told that the actual value of x, to be rev
at the end of the experiment (it was actually 500), was written on the back
piece of paper that was visibly placed on a table and left untouched until th
of the experiment.
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UNDERSTANDING SOCIAL PREFERENCES 829
TABLE I
GAME-BY-GAME RESULTS
Two-person dictator games Left Right
Berk29 (26) B chooses (400,400) vs. (750,400) .31 .69
Barc2 (48) B chooses (400,400) vs. (750,375) .52 .48
Berkl7 (32) B chooses (400,400) vs. (750,375) .50 .50
Berk23 (36) B chooses (800,200) vs. (0,0) 1.00 .00
Barc8 (36) B chooses (300,600) vs. (700,500) .67 .33
Berkl5 (22) B chooses (200,700) vs. (600,600) .27 .73
Berk26 (32) B chooses (0,800) vs. (400,400) .78 .22
Two-person response gamesB's
payoffs identical Out Enter Left Right
Barc7 (36) A chooses (750,0) or lets B choose .47 .53 .06 .94
(400,400) vs. (750,400)
Barc5 (36) A chooses (550,550) or lets B .39 .61 .33 .67
choose (400,400) vs. (750,400)
Berk28 (32) A chooses (100,1000) or lets B .50 .50 .34 .66
choose (75,125) vs. (125,125)
Berk32 (26) A chooses (450,900) or lets B .85 .15 .35 .65
choose (200,400) vs. (400,400)
Two-person response gamesB's
sacrifice helps A Out Enter Left Right
Barc3 (42) A chooses (725,0) or lets B choose .74 .26 .62 .38
(400,400) vs. (750,375)
Barc4 (42) A chooses (800,0) or lets B choose .83 .17 .62 .38
(400,400) vs. (750,375)
Berk21 (36) A chooses (750,0) or lets B choose .47 .53 .61 .39
(400,400) vs. (750,375)
Barc6 (36) A chooses (750,100) or lets B choose .92 .08 .75 .25
(300,600) vs. (700,500)
Barc9 (36) A chooses (450,0) or lets B choose .69 .31 .94 .06
(350,450) vs. (450,350)
Berk25 (32) A chooses (450,0) or lets B choose .62 .38 .81 .19
(350,450) vs. (450,350)
Berkl9 (32) A chooses (700,200) or lets B choose .56 .44 .22 .78
(200,700) vs. (600,600)
Berkl4 (22) A chooses (800,0) or lets B choose .68 .32 .45 .55
(0,800) vs. (400,400)
Barcl (44) A chooses (550,550) or lets B choose .96 .04 .93 .07
(400,400) vs. (750,375)
Berkl3 (22) A chooses (550,550) or lets B choose .86 .14 .82 .18
(400,400) vs. (750,375)
Berkl8 (32) A chooses (0,800) or lets B choose .00 1.00 .44 .56
(0,800) vs. (400,400)
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830 QUARTERLY JOURNAL OF ECONOMICS
TABLE I
(CONTINUED)
Two-person response gamesB's
sacrifice hurts A Out Enter Left Right
Barcll (35) A chooses (375,1000) or lets B .54 .46 .89 .11
choose (400,400) vs. (350,350)
Berk22 (36) A chooses (375,1000) or lets B .39 .61 .97 .03
choose (400,400) vs. (250,350)
Berk27 (32) A chooses (500,500) or lets B .41 .59 .91 .09
choose (800,200) vs. (0,0)
Berk31 (26) A chooses (750,750) or lets B .73 .27 .88 .12
choose (800,200) vs. (0,0)
Berk30 (26) A chooses (400,1200) or lets B .77 .23 .88 .12
choose (400,200) vs. (0,0)
Three-person dictator games Left Right
Barcl0 (24) C chooses (400,400;) vs. (750,37
Barcl2 (22) C chooses (400,400;) vs. (1200,0x) .82 .18
Berk24 (24) C chooses (575,575,575) vs. (900,300,600) .54 .46
Three-person response games Out In Left Right
Berkl6 (15) A chooses (800,800,800) or lets .93 .07 .80 .20
C choose (100,1200,400) or
(1200,200,400)
Berk20 (21) A chooses (800,800,800) or lets .95 .05 .86 .14
C choose (200,1200,400) or
(1200,100,400)
Numbers in parentheses show (A,B) or (A,B,C) money payoffs.
our central findings as they pertain to aspects of social
ences discussed in the previous section. In our general a
we will gloss over many plausibly important issues and a
tive hypotheses about what explains the behavior we obs
particular games.19 While it is of course somewhat arbit
compare models on this set of games, this set clearly o
greater variety of games than much of the previous literatu
each pair of hypotheses about social preferences, we hav
where these preferences make different predictions, and o
in our experimental design was to create a diverse list o
19. In Charness and Rabin [1999] we provide endless play-by-play c
tary interpreting the results, emphasizing especially how the selection
we chose might affect our overall results, and discuss how hypothes
arguing against could be reconciled with the observed behavior.
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UNDERSTANDING SOCIAL PREFERENCES 831
giving scope for the widest array of social motivations to play
and providing scope for the models to fail.
IV. EXPLAINING BEHAVIOR BY DISTRIBUTIONAL PREFERENCES
In this section we compare the power of self-interes
distributional models (competitive, difference-averse, and soc
welfare) to explain our data. We mostly consider how man
servations in our games are consistent with the values of p a
permitted by the restrictions for each type of social prefere
when excluding reciprocity by imposing the restriction 0
This approach accommodates any parameter values withi
relevant range restrictions, permitting individual heterog
for these values without estimating specific values for the
rameters. At the end of the section we analyze the data
positing fixed underlying preferences which subjects implem
with error, estimating the best-fit values of p and a.
Table II shows the explanatory power of various mod
under the appropriate restrictions for p and U.21 As we are n
considering reciprocity motivations, which may influence pr
ences in response games, it is most appropriate to make comp
sons using only the seven dictator games. The first line indic
that social-welfare preferences are far more effective tha
others in explaining behavior when reciprocity issues are abs
Discussing some individual dictator games provides so
intuition for our findings. Berk29, in which B chooses be
(750,400) and (400,400), shows that a substantial number of
subjects refuse to receive less than another person when such
refusal is costless, and provides the strongest evidence in our data
20. In the 19 two-person games where both players make a decision, each
participant makes a choice (in separate cases) as both a first-mover and a responder.
Tracking each person's combination of play might tell us something
about both participants' beliefs about other players' choices, and the motivations
behind their own choices. This is a potentially important source of evidence, and
we present the data in Appendix 3. We discuss these data in Charness and Rabin
[1999]. Beyond showing that behavior in the A role is correlated with behavior in
the B role, we found relatively little of interest. Observed correlations appeared
typically to be compatible with many different models.
21. Our determination of which choices are consistent with which models,
upon which we base the following statistics, is shown in Appendix 4. Because we
include narrow self-interest as a special case of each of the other distributional
preferences, the number of choices consistent with any of these classes of preferences
will be at least as large as the number consistent with narrow self-interest
in games without exact ties. In the many games in which B's payoffs for his two
options are the same; however, each of these models is a restriction on selfinterest,
and hence the numbers we report are variously larger and smaller than
the numbers for narrow self-interest.
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832 QUARTERLY JOURNAL OF ECONOMICS
TABLE II
CONSISTENCY OF BEHAVIOR WITH DISTRIBUTIONAL MODELS
Total # Narrow Difference Social
observations self-interest Competitive aversion welfare
B's behavior in the 232 158 140 175 224
dictator games (68%) (60%) (75%) (97%)
B's behavior in the 671 532 439 510 612
response games (79%) (65%) (76%) (91%)
B's behavior in all games 903 690 579 685 836
(76%) (64%) (76%) (93%)
A's behavior, any 671 636 579 671 661
predictions by A (94%) (86%) (100%) (99%)
A's behavior, correct 671 466 488 603 649
predictions by A (69%) (73%) (90%) (97%)
All behavior, any 1574 1326 1158 1356 1497
predictions by A (84%) (74%) (86%) (95%)
All behavior, correct 1574 1156 1067 1288 1485
predictions by A (73%) (68%) (82%) (94%)
for difference aversion. But note tha
provides the best possible chance of
difference aversion, since it eliminat
thing else as a countervailing motive
subjects exhibiting difference aversion
our data.22 In games where pursuing P
aversion would require sacrifice, we s
Berk23, for instance, which tests the r
of participants to reject offers of the
matum-game experiments, 0 of 36 B's
The remaining two-player dictator
ingness to sacrifice to help A. Barc2 an
between (400,400) and (750,375) provi
aversion. About one-half of B's sacrific
deficit with respect to A. Berk8 and B
willingness by B to help A, where this
difference aversion and social-welfar
in behavior between Barc8 and Berkl5
22. And it should be noted that this one-third
competitive preferences.
23. However, inducing negative reciprocity m
choice did not lead to very high rejection rate
evidence that punishment in the ultimatum gam
aversion.
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UNDERSTANDING SOCIAL PREFERENCES 833
less willing (p x .00) to sacrifice 100 to help A by 400 w
doing so she receives a lower payoff than A.24,25
In this and the other comparisons in Table II, the propo
of observations explained by social-welfare preferences is s
cantly higher than the proportions explained by the other
types of preferences. Except for the case of unrestricted A
ior, all the comparisons between social-welfare prefere
the other three categories would be statistically signific
.00 if each observation were treated as independent.26
These proportions compare how the distributional mode
in explaining all behavior. But when both choices are co
with a model, its ability to match the data may merely re
lack of predictive power. In this light, perhaps a more
test is how well a model matches behavior when it makes a
unique prediction. Note that, because each model embeds self
interest, it makes a unique prediction only when there is an exac
tie in payoffs or when the distributional preference matches sel
interest. Table III shows how each model performs in our data in
each class of choices among those choices where only one of t
two choices is compatible with the model. Again, we see that
social-welfare preferences substantially outperform the oth
models.
Line 1 shows that social-welfare preferences clearly outperform
both difference aversion and competitive preferences in dictator
games. Of course, one may desire a model that does better
than to explain accurately the behavior in dictator games. Distributional
models may be appropriate in response games where
reciprocity is likely to be aroused, either because reciprocity is
relatively weak or because the models are meant to be proxies for
reciprocity.27 We discuss the specific findings on the various types
24. Throughout this and subsequent sections, the p-value is approximated to
two decimal places and is calculated from the test of the equality of proportions,
using the normal approximation to the binomial distribution (see Glasnapp and
Poggio [1985]), and assuming that each binary choice is independent. As we
generally have a directional hypothesis, the p-value given reflects a one-tailed
test, but we use the two-tailed test (and say so) where there is no directional
hypothesis.
25. A higher proportion of B's take a 100 percent share in Berk26 than in
traditional dictator experiments. But the 22 percent rate observed for even splits
is not unusual in a dictator game, and no intermediate split was available.
26. If we assume that each individual's choices are only one independent
observation, we can calculate a minimum level of statistical significance by dividing
the test statistic by /8, since we can have as many as eight observations for
each individual. Doing so, we find statistical significance at p < .05 in each case
except for unrestricted A behavior.
27. One possibility, for instance, is that difference aversion may not be
literally correct, but may be a parsimonious proxy for complicated intentionsThis
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834 QUARTERLY JOURNAL OF ECONOMICS
TABLE III
CONSISTENCY OF BEHAVIOR WITH DISTRIBUTIONAL MODELS
WHEN THE PREDICTION IS UNIQUE
(Entries are chances taken over total chances.)
Narrow Difference Social
Class of games self-interest Competitive aversion welfare
B's behavior in the dictator 132/206 104/196 49/106 54/62
games (64%) (53%) (46%) (87%)
B's behavior in the response 346/479 319/551 350/517 304/363
games (72%) (58%) (68%) (84%)
B's behavior in all games 478/685 423/747 399/623 358/425
(70%) (57%) (64%) (84%)
A's behavior, any 172/226 212/304 32/32 74/84
predictions (76%) (70%) (100%) (88%)
A's behavior, correct 466/671 364/553 181/249 134/150
predictions (69%) (66%) (73%) (89%)
All behavior, any predictions 650/911 635/1051 431/655 432/509
by A (71%) (60%) (66%) (85%)
All behavior, correct 944/1356 787/1300 580/872 492/575
predictions (70%) (61%) (67%) (86%)
of response games in the next section
and Table III shows that social-welf
narrow self-interest outperform diff
tive preferences. Line 3 of both table
B behavior.
While we have emphasized B's behavior in reaching our
strongest conclusions, obviously A's behavior may also be motivated
by social preferences. Interpreting A behavior is more problematic,
since A's perceived consequences of his choice depend on
his beliefs about what B will do. One approach is to make no
assumptions about what A believes B will do-and say that A's
choice is consistent with a restriction on preferences if his choice
is consistent given any belief about what B might do. A stronger,
more common, and more tenuous way to interpret A's choices is to
assume that A's correctly anticipated the empirically observed
responses by B's and hence that A's made a binary choice between
that expected payoff and the payoff from the outside option.
Appendix 4 presents our classification of A's choices in all the
based reciprocity models. However, as demonstrated by Tables II and III, and
especially Table IV below, our experiments call into question even this weaker
case for difference aversion.
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UNDERSTANDING SOCIAL PREFERENCES 835
two-player response games using each of these two methods,
Tables II and III assess A's behavior using both methods.
Referring to Table II, under the liberal interpretation
consistency, few choices by A are entirely inconsistent with an
the models, but clearly difference aversion and social-we
preferences do very well, narrow self-interest does a little w
and competitiveness does relatively poorly. The more restr
consistency interpretation seems to indicate the superiori
social-welfare preferences. However, we urge caution in m
this interpretation, as there are more observations where
tively implausible parameter values are needed to reconci
choices with social-welfare preferences than with differ
aversion.
The behavior by A's in our experiments helps shed light on
the stylized fact, much emphasized over the years, that observed
generosity by proposers in ultimatum games is not discernibly
inconsistent with narrow self-interest, since "generous" offers are
an optimizing response to fear of having their offers rejected by
responders. It is not clear what the generalization of this fact
would be beyond the ultimatum game, but the hypothesis that
first-mover behavior is approximately self-interested is (as with
many hypotheses) not sustainable when analyzing games besides
the ultimatum game. In our data, 27 percent of A's take the action
that, given actual B behavior, involved an expected sacrifice. By
this measure, A behavior is less self-interested than B behavior.
While this could, of course, be an artifact of misprediction by A's,
note that of A's whose sacrifice helps B, 35 percent sacrificed,
whereas only 15 percent sacrificed to hurt B's. This difference
(179/517 vs. 22/144) is significant atp - .00. Even more directly,
note that in the eight games in which A's decision to enter could
only lose her money but could help B, 33 percent (92/276) sacrificed.
In the two cases where entry by A could not help either
player, 19 percent (10/52) entered.28 Tables II and III show that,
depending on how one measures it, departures from self-interest
are just as common for A's as for B's.
The last two rows of Tables II and III tally up the consistency
of all choices in two-player games by adding A's choices to B's
28. The eight games where entry could help B are Barc4, Barc6, Barc7,
Barc9, Berkl4, Berkl9, Berk21, and Berk25; the two games where it hurts (given
B's actual behavior) both are Berk30 and Berk32.
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836 QUARTERLY JOURNAL OF ECONOMICS
TABLE IV
B's SACRIFICE RATE BY EFFECT ON INEQUALITY
Sacrifices/ Probability
Class of games chances of sacrifice
Games allowing Pareto-damage 59/357 17%
Decreases inequality 34/228 15%
No effect on inequality 4/35 11%
Increases inequality 21/94 22%
Games where sacrifice helps A 199/546 36%
Decreases inequality 99/212 47%
No effect on inequality 8/68 12%
Increases inequality 92/266 35%
All games 268/903 30%
Decreases inequality 133/440 30%
No effect on inequality 12/103 12%
Increases inequality 123/360 34%
Games allowing Pareto damage are 5, 7, 11, 22, 23, 27,
Games in which a sacrifice helps A are 1, 2, 3, 4, 6, 8,
choices in the second row, and me
of the two methods discussed above.29
Table IV shows a useful way to parse our results to help see
why difference aversion performs poorly, breaking down both
Pareto-damaging and helpful behavior by B into its effects on
inequality. Overall, B's engage in Pareto-damaging behavior in
17 percent of their opportunities to do so. More interestingly, in
our sample B's are less likely to cause Pareto damage when this
decreases inequality than when Pareto damage increases inequality.
We do not believe that this would be the pattern more
generally, but combined with the overwhelming confound between
inequality reduction and Pareto-damaging behavior even
in previous research that disentangles Pareto damage from negative
reciprocity, this further calls into question the strong link
implied by difference-aversion models between sacrifice and
inequality-reduction.
B sacrifices to help A 36 percent of the time when he has the
29. As the number of participants in each game varied, our percentages in
Tables II and III (and elsewhere) could be correspondingly influenced by weighting
different games differently. Thus, we also checked these percentages by
assigning an equal weight to each game form. We find that the percentages
changed very little-with this approach, the penultimate row of Table II becomes
84 percent, 73 percent, 87 percent, 94 percent, and the last row becomes 73
percent, 67 percent, 82 percent, 94 percent.
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UNDERSTANDING SOCIAL PREFERENCES 837
TABLE V
DISTRIBUTIONAL MODELS AS EXPLANATIONS FOR B'S SACRIFICE
Sacrifices/ Probability
Class of games chances of sacrifice
All games where B can sacrifice 213/737 29%
When sacrifice is...
Consistent with competitive 10/156 6%
Inconsistent with competitive 203/581 35%
Consistent with DA 108/332 33%
Inconsistent with DA 105/405 12%
Consistent with SWP 191/478 40%
Inconsistent with SWP 22/259 8%
Consistent with DA but not SWP 9/120 8%
Consistent with SWP but not DA 92/266 35%
Games where B can sacrifice are 1, 2, 3, 4, 6, 8, 9, 11, 13, 14, 15, 17,
opportunity to do so. There is a signific
between helping behavior and whether s
decreases inequality, consistent with the p
ference aversion and social-welfare pref
overall, 34 percent of inequality-increas
rifice are taken, however, indicates muc
social-welfare preferences than for dif
flected in the statistics reported in Tab
A final test of the consistency of ou
distributional models is to parse results ac
different models predict sacrifice behavio
where B is indifferent. This can provi
strength of the different social motivatio
tions conflict with self-interest. Table V
also directly compares social-welfare pr
aversion when the two models make dif
sacrifice.30
Table V shows that B sacrifices 40 percent of the time when
doing so is consistent with social-welfare preferences, but only 8
percent of the time when a sacrifice is inconsistent with socialwelfare
preferences. The last two rows strongly suggest that
social-welfare preferences play a more prominent role in B's decision
to sacrifice money, although caution must be used, since in
30. It is clear that competitive preferences do a poor job of explaining sacrifices
by B.
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838 QUARTERLY JOURNAL OF ECONOMICS
our set of games the average sacrifice needed to promote difference
aversion is greater than that needed to promote socialwelfare
preferences.31
If interpreted as error-free reflections of stable behavior,
these experiments that test distributional preferences when no
self-interest is at stake indicate that something like 70 percent of
choices can be attributed to social-welfare-maximization, 20 percent
to difference aversion, and 10 percent to competitiveness.
Results from Charness and Grosskopf [2001], in which a small
amount of money was at stake, are perhaps even more telling.
While 67 percent of 108 subjects chose (Other, Self) payoffs of
(1200,600) over (625,625), only 12 percent chose payoffs of
(600,600) over (1200,625). That is, of the two-thirds of subjects
who had social-welfare rather than difference-averse or competitive
preferences, virtually all were willing to sacrifice 25 pesetas
to implement those preferences. Of the one-third of subjects who
had either difference-averse or competitive preferences, twothirds
were unwilling to sacrifice 25 pesetas to implement those
preferences.
Our comparisons of models above assume that all behavior
reflects stable underlying preferences of the individual, and then
analyzes the frequency of different preferences that can explain
the data. We turn now to an approach to summarizing our data
that assumes that all subjects share a fixed set of preferences,
and that observed behavior corresponds to individuals implementing
those preferences with error. The likelihood of error is
assumed to be a decreasing function of the utility cost of an error.
We estimate the population means for p and a in the Section II
equations (excluding reciprocity as an explanatory variable by
imposing the restriction 0 = 0) by performing maximum-likelihood
estimation on our binary-response data using the logit
regression
31. Similar evidence from elsewhere also supports our findings about the
relative frequency of behavior consistent with social-welfare preferences, difference
aversion, and competitiveness. Charness and Grosskopf [2001] found that
while about 33 percent of subjects chose (Other, Self) allocations of pesetas of
(600,600) over (900,600), about 11 percent of subjects chose (Other, Self) allocations
of (400,600) over (600,600). This suggests that about one-third of subjects
who chose to equalize payoffs when behind are competitive rather than difference
averse. In a variant where each of 108 choosers receives 600 but can choose any
payoff for the other person between 300 and 1200, 74 percent chose 1200, 7
percent chose a number between 600 and 1200, 10 percent chose 600, and 8
percent chose a number less than 600.
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UNDERSTANDING SOCIAL PREFERENCES 839
e u(acttonl)P(action 1) actol + act (action2)
P(action 1) = e-y u(acton 1 ey -u(action2)
to determine the values that best match predicted probabilit
play with the observed behavior. The precision parameter
flects sensitivity to differences in utility, where the higher
value of y, the sharper the predictions (see McFadden [1
When y is 0, the probability of either action must be 50 per
when y is arbitrarily large, the probability of the action yie
the highest utility approaches 1.
We estimate the values in these equations by imposing
ther restrictions on parameters implied by the variety of m
that can be encompassed within this framework, using th
for B behavior in all games.32 Since we have the same numbe
observations in each case, in addition to observing the esti
value of y in each of our models, we can compare the loghood
values to gain some insight into the explanatory po
the parameters and the models.
This approach allows us to compare models that make
ferent predictions about the parameter values, and to investi
the power of different models and the costs of the restriction
impose. While the allowance for "noise" in maximizing ut
provides a proxy of sorts for the heterogeneity that cer
exists among participant's parameter values, it does so o
crudely.33 As such, we believe that our regression results pr
a strong indication of general patterns in our data and help s
among models, but are not adequate for grasping an acc
sense of the relative frequency of preferences that describe
sets of the subjects. Moreover, while we have chosen a br
array of games than any previous papers with which we
familiar, as with all previous empirical tests of social-prefer
models, the fitted values for these parameters is influenced b
choice of games to study.
Table VI reports the regression results for a variety of dif
ent restrictions on the parameter values. In the first line
report how well the pure self-interest model fits the dat
rather low level of precision, as measured by either -y
log-likelihood, serves as a benchmark for the other mode
32. We follow an approach similar to that used in Charness and Haru
[1999].
33. Estimation of separate p and a values for each individual would be
difficult, since the number of observations for each individual is little more than
the number of parameters to be estimated.
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840 QUARTERLY JOURNAL OF ECONOMICS
TABLE VI
REGRESSION ESTIMATES FOR B BEHAVIOR (N = 903)
Model Restrictions p a 0 y LL
Self-interest p = 0 = 0 - - - .004 -593.4
(9.07)
Single parameter-- p = , 0 = 0 .212 .212 - .005 -574.5
"altruism" (7.20) (7.20) (8.65)
Single parameter- p = 0 = 0 .118 - .004 -591.5
"behindness aversion" (1.76) (8.53)
Single = 0 = 0 .422 - - .014 -527.9
parameter-"charity" (25.5) (11.6)
p,a model without 0 = 0 .423 -.014 - .014 -527.7
reciprocity (25.5) (-0.73) (11.6)
"Reciprocal charity" = 0 .425 - -.089 .015 -523.7
(27.9) (-2.98) (11.3)
p,a model with none .424 .023 -.111 .015 -523.1
reciprocity (28.3) (1.10) (-3.11) (11.6)
t-statistics are in parentheses y is the precision parameter, and L
Games where A's entry is SWP-misbehavior are 1, 5, 11, 13, 22, 2
next three lines report on three differe
additional parameter to account for a pe
payoffs of others. On line 2, we investig
model that has been employed sporadic
economists-that says B cares about a we
payoffs and A's payoffs. This model has cl
beyond the pure self-interest model, lowe
and marginally raising y. The estimation
best-fit single parameter has B putting sig
on A's payoff.
Lines 3 and 4 examine how well a model would fit if we
restricted a person's concern for the other to the case where,
respectively, she is behind the other or she is ahead. Line 3
imposes the restriction that p = 0, accommodating the model
developed by Bolton [1991] to match the data in the ultimatum
and other bargaining games. The results show that this model 1)
does significantly worse than the simple altruism model, and has
no significant explanatory power beyond pure self-interest, and 2)
that the best fit value of u is positive, rather than negative as
posited by Bolton.34 As argued in different ways above, this too
34. But it is only marginally significant, and it seems clear that it is significantly
greater than 0 only because of the imposed restriction that p = 0. In some
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UNDERSTANDING SOCIAL PREFERENCES 841
helps indicate that those models built on the assumption that
0 do not usefully organize the data on broad sets of games wh
this hypothesis for Pareto-damaging behavior is not confou
with other explanations. Line 4 tests the "charity" model, w
posits that people only care about the payoff of those others
receive less than they do. As can be seen, this model does sign
cantly better than altruism or pure self-interest, indicating t
there is indeed much less concern for those who are getti
better payoff.
Indeed, Line 5, in which we estimate the linear distributio
model without restrictions, explains the data no better tha
charity model does. The estimated value of a is very small
insignificantly different from 0, so that the estimate of p is v
ally identical whether or not u is included. Along with the sm
changes in the log-likelihood and y estimates, we see that nei
difference aversion nor social-welfare preferences are sig
cantly better models of distributional preferences than the s
pler charity model.
Overall, the major gains in explanatory power come f
allowing p to vary independently of a. In lines 4-6 the lo
likelihood is much better, and the precision is much greater.
4 indicates that people tend to be charitable toward those who
less fortunate, but feel different when such charity woul
increase the minimum of the players' material payoffs. Li
and 5 together show that (overall, and absent A's misbehavior
is not much of a driving force in our games. Removing the res
tion that u = 0 gains us very little: although the likelihood
goes down slightly, a significance test gives x2 = .54, far from
5 percent significance level of 3.84. Thus, any explanation
nonpecuniary behavior that relies upon u being typically nega
seems inadequate.
V. THE ROLE OF RECIPROCITY
In this section we analyze our results in terms of evidence for
reciprocity. We designed our experiments so as to have many
examples of games with identical choices for B following different
choices by A, or no choice by A. By comparing the selection B
makes from identical choice sets as a function of the choice A
games either parameter could explain behavior, and hence it appears that a is
reflecting the positive value of p in those games.
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842 QUARTERLY JOURNAL OF ECONOMICS
previously did or did not make, we gather very direct evidence on
the role of reciprocity in explaining responder behavior. We first
discuss specific games to give an intuitive sense of the behavior
observed. We then present some aggregate statistics examining
B's response as a function of A's behavior, and conclude the
section with regression analysis estimating the reciprocity parameter
0 in the model of Section II.
Our three games in which B chooses between (750,400) and
(400,400) are especially informative:
Games with the choice between
(400,400) and (750,400) (400,400) (750,400)
Berk29 (26) B chooses (400,400) vs. (750,400) .31 .69
Barc7 (36) A chooses (750,0) or lets B choose .06 .94
(400,400) vs. (750,400)
Barc5 (36) A chooses (550,550) or lets B choose .33 .67
(400,400) vs. (750,400)
Most interesting is the difference between Barc7 and Berk29,
which is significant at p - .00. This comparison can be seen as
testing the relative strength of positive reciprocity versus difference
aversion when self-interest is not implicated. In contrast to
the 31 percent of B's who choose (400,400) in the dictator game
Berk29, only 6 percent do so following a generous move by A.35
Because B's choice between (750,400) and (400,400) is a strong
invitation to B to pursue difference aversion, and (as we show
below) positive reciprocity is nowhere else a strong motivation in
our data, the weakness of difference aversion here indicates that
it is not a strong factor when in conflict with other social motivations.
The results from Barc5 surprised us, as B's were no more
likely than in Berk29 to choose (400,400). Punishment for the
unfair entry by A would be free here, yet is not employed.
Turning to games where B can sacrifice to help A, consider
first those games letting B choose between (400,400) and
(750,375).
Games with the choice between
(400,400) and (750,375) (400,400) (750,375)
Barc2 (48) B chooses (400,400) vs. (750,375) .52 .48
35. Note that the dictator version was in Berkeley, not Barc
did not run a (400,400) vs. (750,400) dictator game in Barcelona,
Grosskopf result of 34 percent vs. 66 percent in the (600,600) vs.
game in Barcelona was quite similar to the 31 percent vs. 69
Berk29.
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UNDERSTANDING SOCIAL PREFERENCES 843
Berkl7 (32) B chooses (400,400) vs. (750,375) .50 .50
Barc3 (42) A chooses (725,0) or lets B .62 .38
choose (400,400) vs. (750,375)
Barc4 (42) A chooses (800,0) or lets B .62 .38
choose (400,400) vs. (750,375)
Berk21 (36) A chooses (750,0) or lets B .61 .39
choose (400,400) vs. (750,375)
Barcl (44) A chooses (550,550) or lets B .93 .07
choose (400,400) vs. (750,375)
Berkl3 (22) A chooses (550,550) or lets B .82 .18
choose (400,400) vs. (750,375)
The games in which B chooses between (400,400) and
(750,375) provides the starkest illustration of our two main findings
about reciprocity. A large percentage of B's here are willing
to sacrifice to pursue the social-welfare-maximizing allocation
when they feel neutral toward A's. There is clearly no evidence of
positive reciprocity in comparing Barc2 and Berkl7 to Barc3,
Barc4, and Berk21.36 B is in fact less likely to sacrifice in pursuit
of the social-welfare-maximizing outcome following kind behavior
by A than in the dictator context (the difference is collectively
significant in a two-tailed test at p .14). However, we see
evidence of concern withdrawal: B is likely to withdraw his willingness
to sacrifice to give the social-welfare-maximizing allocation
to A if A has behaved selfishly. Comparing within subject
pools, the percentage of B's who sacrifice to help A following a
selfish action drops from 48 percent to 7 percent (from Barc2 to
Barcl) and from 50 percent to 18 percent (from Berkl7 to
Berkl3). These differences are both significant at p < .01.
The lack of positive reciprocity also shows up when comparing
Barc6 to Barc8, the games where B chooses (300,600) vs.
(700,500) and (200,700) vs. (600,600), and Berkl5 to Berkl9.
Games where B chooses between
(300,600) and (700,500) (300,600) (700,500)
Barc8 (36) B chooses (300,600) vs. (700,500) .67 .33
Barc6 (36) A chooses (750,100) or lets B choose .75 .25
(300,600) vs. (700,500)
36. We note in passing that this lack of positive reciprocity is consistent with
results from trust games (e.g., Berg, Dickhaut, and McCabe [19951) and giftexchange
games, which are often interpreted as positive reciprocity. The decision
by responders to "return" some money given to them seems typically consistent
with the type of sharing we find in dictator games.
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844 QUARTERLY JOURNAL OF ECONOMICS
Games where B chooses between
(200,700) and (600,600) (200,700) (600,600)
Berkl5 (22) B chooses (200,700) vs. (600,600) .27 .73
Berkl9 (32) A chooses (700,200) or lets B choose .22 .78
(200,700) vs. (600,600)
The set of games where B chooses between (400,400) and
(0,800) provides a confusing picture about the role of positive
reciprocity.
Games where B chooses between
(0,800) and (400,400) (0,800) (400,400)
Berk26 (32) B chooses (0,800) vs. (400,400) .78 .22
Berkl4 (22) A chooses (800,0) or lets B choose .45 .55
(0,800) vs. (400,400)
Berkl8 (32) A chooses (0,800) or lets B choose .44 .56
(0,800) vs. (400,400)
The results from Berkl4, where 55 percent choose (40
(0,800) in contrast to the 22 percent who choose (400,
dictator game Berk26, significant at p .01, would seem to
indicate positive reciprocity. But the results from Berkl8 call this
interpretation into question. We thought B's willingness to sacrifice
would be roughly equal to that in the dictator version of the
game, but it is much greater, significant at p z .01.37
Our final grouping of games where B's payoffs are identical
were meant to test difference aversion as an explanation of Pareto
damage in a simplified form of the ultimatum game.
Games where B chooses between
(800,200) and (0,0) (800,200) (0,0)
Berk23 (36) B chooses (800,200) vs. (0,0) 1.00 .00
Berk27 (32) A chooses (500,500) or lets B choose .91 .09
(800,200) vs. (0,0)
Berk31 (26) A chooses (750,750) or lets B choose .88 .12
(800,200) vs. (0,0)
Zero of 36 subjects chose the (0,0) outcome outside
text of retaliation, while 6/58 chose (0,0) in the two t
where retaliation is a motive. The difference between Berk23 and
each of the other two games is significant separately at p < .06.
37. The only sense we can make of this is that A has unambiguously stated
a preference against the (0,800) payoff, reducing B's ability to rationalize taking
everything. However, this is a weak explanation, and we are puzzled by this
result.
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UNDERSTANDING SOCIAL PREFERENCES 845
TABLE VII
B's RESPONSE AS A FUNCTION OF A's HELP OR HARM
Probability
Class of games Sacrifices/chances of sacrifice
All games allowing Pareto-damage 59/357 17%
A has helped B 2/36 6%
A has had no play 8/62 13%
A has hurt B 49/259 19%
All games where sacrifice by B helps A 199/546 36%
A helped B 100/278 36%
A had no play* 88/202 44%
A hurt B in violation of SWP 7/66 11%
* We include Berkl8 in this classification, since A's decis
But together with Barcll and Barc
can sacrifice to hurt A, we find rela
ity. In all of these games, B has the
following what we felt would be per
decision by A.
Games where B can punish A for
negative reciprocity. As in Barc5, we
ings in Berk28 and Berk32. In each
action by A could be punished for
percent of Bs do so. Doing so cont
ences in Barc5 and both social-welfar
aversion in Berk28 and Berk32. Th
our results: for whatever reason, w
stances of retaliatory decreases in
benefited the retaliators materially.3
As a first pass at summarizing th
Table VII specifies a distributional
positive sacrifice in terms of how A
when A hurts B, B is more likely t
more likely to withdraw willingne
difference in Pareto-damaging B b
when A hurts B is significant at
38. Perhaps the way our games are frame
take-it-or-leave-it aspect of the ultimatum
forgone payoff design (e.g., Brandts and S
bacher [1999] should also share this problem
80/20 proposals.
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846 QUARTERLY JOURNAL OF ECONOMICS
when A hurts B and when A either has no play or helps B is also
significant at p : .02.
B sacrifices to help A 36 percent of the time when he has the
opportunity to do so. The data support the view that positive
reciprocity plays little role in helping behavior, and that negative
reciprocity, particularly concern withdrawal, does play a role. The
table crystallizes the fact that our data show that a nice prior
choice by A is less likely to yield nice treatment by B than is no
choice by A at all-reducing helping behavior from 44 percent to
36 percent. By contrast, when A has hurt B, helping behavior
reduces to 11 percent. Hence, we see that violation of socialwelfare
norms plays a stronger role in determining when a person
sacrifices to help another player than it plays in determining
when a player sacrifices to harm another. While involving only
two games and 66 observations, this last comparison forms part of
the basis for our incorporation of "concern withdrawal" as the
primary form of reciprocity in our formal model developed in
Appendix 1.
To give a more precise analysis of the role of reciprocity,
consider the bottom two lines of Table VI, which remove the
constraint on our regression analysis that 0 = 0, the parameter
measuring how "social-welfare misbehavior" by A affects B's
weight on A's payoff. The level of precision (y) is much higher for
each of these reciprocity regressions than for the self-interest
model regression. More importantly, lines 5, 6, and 7 together
show that reciprocal motivations play a greater role in behavior
than do nonreciprocal preferences to either help or hurt those
who are ahead.39 Comparing lines 5 and 7 shows that the estimate
of 0 is significantly negative; the likelihood-ratio test gives
X2 = 9.18 (p ; .00).40 Note that this is much stronger than
allowing a to vary; comparing lines 6 and 7, for instance, does not
produce a substantial difference: the other parameter values do
not change much, and the likelihood-ratio test gives x2 = 1.26 (not
significant, p .27). Once one includes reciprocity in the regres-
39. Although our definition of "misbehaved" builds on social-welfare preferences,
we note that results are quite similar when q reflects misbehavior by
difference-aversion standards, as built into the reciprocity model developed by
Falk and Fischbacher [1998]. While games such as Berk28 and Berk32 look highly
suggestive to us as indications that it is violations of social-welfare preferences
that trigger retaliation, our formal analysis does not support either model against
the other.
40. Although the multiple-observation caveat to statistical significance may
still apply, a comparison between the likelihood-ratio tests nevertheless indicates
that allowing 0 to be nonzero has a much greater impact than allowing a to be
nonzero.
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UNDERSTANDING SOCIAL PREFERENCES 847
sions, allowing for players with lower payoffs to care (po
intrinsically about the payoff of the other player has som
not much, explanatory power.
All said, an analysis over a broad range of games in
that reciprocity considerations are an important comp
behavior.
VI. MULTIPERSON GAMES
Although we emphasize two-player distributional preferences
throughout the paper, we also ran several games with three
players, whose results shed light on the issues discussed in previous
sections, and on hypotheses specific to three-player games.
While the model discussed in Section II and tested above relates
to two-person games, it is motivated by the more general multiperson
model that is outlined in Appendix 1. Of special interest in
multiperson models are questions about how players feel about
changes in the distribution among others' payoffs. We presume
that B cares more about A's payoff when A earns less than B than
when A earns more. This is the two-player projection of the more
general notion that (absent negative reciprocity and in addition to
self-interest) people like to improve the payoffs of everybody, but
are more concerned about raising the payoffs of those with lower
payoffs. In simplified and extreme form, they like to maximize the
minimum payoff among players.
Barcl0 and Barcl2 offer a test of people's "disinterested"
views of fairness. The results indicate that people care about both
the total surplus and the minimum payoff among others. In both
cases, many subjects chose to increase total surplus at the expense
of minimum payoff, while others chose to maximize the
minimum payoff. The results in Barcl0 are of special interest in
light of our two-player results. Our results above show that about
50 percent of B's choose (400,400) over (750,375), consistent with
those subjects being different-averse, self-interested, or competitive.
None of these motivations would explain the choice by C's to
choose (400,400), suggesting that a good proportion of Bs are
choosing (400,400) for "disinterested" social-welfare reasons
rather than just to get more money. Barcl0 and Barcl2 together
show that social efficiency is not the only distributional driving
force, as (1200,0,x) is more socially efficient than (750,375,x),
but is chosen much less frequently (p - .01).
Bolton and Ockenfels [2000] assume that social preferences
extend only to the average payoff of all other players, so that
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848 QUARTERLY JOURNAL OF ECONOMICS
people are unconcerned with the distribution of those payoffs.
Bolton and Ockenfels [1998, 2000] provide examples from Gtith
and van Damme [1998] and elsewhere, in which players seem
relatively unconcerned with the distribution of payoffs among
other parties. Because we did not believe that rejections in the
ultimatum game are a manifestation of distributional preferences
rather than reciprocity, and more generally found it surprising to
posit that subjects were indifferent to the allocations among
others, we designed Berk24 as a simple and direct test of their
hypothesis.41
Berk24 demonstrates that subjects care about the allocation
among other parties: 54 percent of the participants sacrificed 25 to
equalize payoffs with each of the other players, without changing
the difference (zero) between a player's own payoff and the average
of other players. Under the assumption that virtually no participants
would (without reciprocal motivations) choose (575,575,575)
over (600,600,600), these results are consistent with both socialwelfare
preferences and Fehr and Schmidt's [1999] difference aversion,
but are inconsistent with Bolton and Ockenfels' [2000] difference
aversion. Since the sacrifice involved is small, it may be hard to
say how strong the motive is. In the context of our other results,
however, we are not inclined to call it small: 54 percent is a higher
proportion than we found are inclined to sacrifice nothing to eliminate
disadvantageous inequality against themselves. Hence, our
results suggest that people are more concerned about this aspect of
the distribution among other players' payoffs than about equalizing
the self-other payoffs in the sense captured by difference-aversion
models.
Finally, our two three-person response games also offer
strong evidence of reciprocity in responder behavior. Berkl6 and
Berk20 test the explanatory power of distributional preferences
versus reciprocity, disentangled from self-interest. In both games,
C receives a payoff of 400 regardless of her choice, and has
identical choices among the distribution of the other two players'
41. Kagel and Wolfe [1999] designed a clever variant of a three-person
ultimatum game and find a form of insensitivity to third-party allocations when
the Bolton and Ockenfels [2000] and the Fehr and Schmidt [1999] models of
difference aversion predict high sensitivity to these allocations. The clear interpretation
of Kagel and Wolfe's [1999] data is that the observed insensitivity to
payoff distributions is due not to the functional form of difference aversion (as
claimed by Bolton and Ockenfels [2000]), but rather because difference aversion in
any form does not explain the behavior they discussed. Nevertheless, the willingness
of participants to assign (as a consequence of a rejection) low payoffs (in their
experiment 2) to innocent third parties also goes against social-welfare preferences,
and can only be rationalized as a strong willingness to punish the proposer.
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UNDERSTANDING SOCIAL PREFERENCES 849
payoffs-1200 and 100, or 1200 and 200. While the differe
aversion models make different predictions in these two g
the evidence shows that all of the models are wrong. Notice
the proportion of C's choosing the 1200/400/100 combination
the 1200/400/200 combination jumped from 14 percent
percent when the choice meant A would get the low payoff in
of B. C's were unhappy with A's greed, and chose to give
lower payoff irrespective of the distributional consequences,
ishing A's 83 percent of the time overall. This difference in c
is significant at p .00. Because the differences in distribu
consequences of behavior were minor, we do not consider
good test of the relative strength of distributional versus rec
ity motivations. Rather, it shows that reciprocity can overw
distributional concerns in some circumstances.
VII. SUMMARY AND CONCLUSION
This paper continues recent research delineating the nature
of social preferences in laboratory behavior. Our results suggest
that the apparent adequacy of recent difference-aversion models
has likely been an artifact of powerful and decisive confounds in
the games used to construct these models.42 We find a strong
degree of respect for social efficiency, tempered by concern for
those less well off.
Our data are rich and complicated. We have not analyzed them
exhaustively, nor incorporated all observed patterns into our formal
models. We have not tested for individual differences and correlation
across games, and neither our analysis nor our model deals with
heterogeneity of subject preferences. Nor does our model capture
evidence in the data for what might be called a complicity effect: the
mere fact of one player being involved in a decision seems to make
the other player more self-interested. Perhaps impulses toward prosocial
behavior are diminished when an agent does not feel the full
responsibility for an outcome.43
42. Our view that difference aversion is unlikely to prove to be a strong factor
in laboratory behavior does not mean that we believe comparable phenomena are
unimportant in the real world. Indeed, we suspect the inherent limitations of
laboratory experiments prevent full realization of phenomena-such as jealousy,
envy, and self-serving assessments of deservingness-that are likely to create de
facto difference aversion in the real world. On the other hand, there is also reason
to believe that experimental settings may exaggerate difference aversion since the
very nature of the careful, controlled designs and use of monetary rewards makes
relative payoffs salient.
43. See Charness [2000] for a discussion of responsibility alleviation, and a
review of papers with evidence related to the phenomenon.
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850 QUARTERLY JOURNAL OF ECONOMICS
One benefit of the sort of simple games we study is that it is
easier to discern what subjects believe are the consequences of
their actions. But even in our simple games-and inherently in
games with enough strategic structure to make reciprocity motives
operative--we could not reach sharp conclusions about the
motivations of first movers because we could not be sure how they
thought the responders would play. Hence, we feel one avenue for
experimental research would be to design ways to more directly
discern participants' beliefs about the intentions or likely behavior
of other subjects.44
Most of our evidence strongly replicates others' findings that
positive reciprocity has virtually no explanatory power in many of
the conventional games studied. Yet the data from one game call
into question the generality of this conclusion. In the game Barc7,
the reader will surely recall, A can forgo a (750,0) outcome to give
B the choice between (750,400) and (400,400). Only 6 percent of
Bs choose (400,400). This is only one game in one session with 36
subjects, but the findings are provocative: together with the fact
that 30 percent choose (400,400) following either no move or a
nasty move by A, the 6 percent suggests a possible form of
positive reciprocity that may be very strong compared with difference
aversion. Will subjects who have just been treated kindly
engage in petty acts of Pareto damage just to equalize payoffs?
Our suspicion is that the answer is broadly "no." Even if researchers
eventually conclude that many subjects are difference-averse
when neutral, it may be necessary to develop models where
positive feelings toward another subject can lead them to be
unwilling to harm that subject in pursuit of difference aversion.
We are especially keen to understand the behavior of subjects
in Barc7 and games like it because we think they are a simplified
form of very common social and economic situations: a "wealthy"
party can do something for a less well-off party and hope that
second party will not take advantage of a chance for petty, lowcost
punishment just to hurt her. Indeed, we suspect situations
resembling this game are far more common in the real world than
in situations resembling the ultimatum game. Such games capture
phenomena such as employer-employee bargaining, where
any accepted take-it-or-leave-it wage offer by an employer will be
followed by opportunities for employees to undermine or to en-
44. For example, Dufwenberg and Gneezy [2000] measure both A's expectation
about B behavior and B's expectation about the expectation of A; they find
that B's expectation of A's expectation is positively correlated with B's response.
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UNDERSTANDING SOCIAL PREFERENCES 851
hance the employer's profits. More generally, opportuniti
affect another's payoff at small cost to oneself is important e
nomically, and suggests that reciprocity motives are like
loom large.
All said, it is clear that a broad array of additional games and
methods would be useful for studying social preferences. Clearly,
more research funding is needed.
APPENDIX 1: A MORE GENERAL MODEL
In Appendix 1 we construct a model that integrates socialwelfare
preferences with reciprocity--both concern withdrawal
and negative reciprocity-into a multiperson model of social preferences.
This model gives an interpretation of the underlying
motives that play a role in the two-player games, as well as
extending our analysis to more than two players. The model we
develop omits the many other factors that seem to play a role in
some subjects' choices, and presents general functional forms
allowing many degrees of freedom. Moreover, the model is complicated,
as it formulates reciprocity as a de facto psychological
Nash equilibrium as defined in the framework developed by
Geanakoplos, Pearce, and Stacchetti [1989]. All said, we do not
see it as being primarily useful in its current form for calibrating
experimental data, but rather as providing progress in conceptualizing
what we observe in experiments.
We first define reciprocity-free preferences in two steps, and
add the reciprocity component later. First, consider a "disinterested"
social-welfare criterion:
W('f1,'fi2, . . . , N) = 8 min [il1,2, ... , TNI
+ (1 - )(lrr, + ( T2 + 2 + '-N),
where 8 E (0,1) is a parameter measuring the degree of concern
for helping the worst-off person versus maximizing the total
social surplus.45 Setting 8 = 1 corresponds to a pure "maximin" or
"Rawlsian" criterion, whereby social welfare is measured solely
according to how well off the least well off is. Setting 8 = 0
corresponds to total-surplus maximization.
Now consider Player i's payoffs as a weighted sum of this
45. It would be more realistic (but more complicated) to assume that people
care about not just the lowest payoff, but the full distribution of payoffs, giving
more and more weight to the well-being of those with lower and lower payoffs.
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852 QUARTERLY JOURNAL OF ECONOMICS
disinterested social-welfare criterion (which includes his own
payoff) and his own payoff:
V,(rl1,7r2,. ,TN)- (1 - )' + X'[2min [ rr2,...,rN
+ (1 - 8) ' (1 + + 2 +' '" + g),
where X E [0,1] measures how much Person i cares about pursuing
the social welfare versus his own self-interest. Setting X = 1
corresponds to purely "disinterested" preferences, in which players
care no more (or less) about her own payoffs than others'
payoffs, and setting X - 0 corresponds to pure self-interest.
To see the connection between these preferences and the
two-player specification of Section II when we ignore reciprocity,
note that the above formulation reduces to
VB('TA,'TB) (1 - XB)T+B + XSAA when rB - 7A,
VB(1rA,TB) TB + X(1 - 6)7TA when B- TB 7A.
If we normalize these two equations by dividing by 1 + X(1 - 8),
so that as in the Section II model VB = TB when TB, = A, we see
that p = X/(1 + X(1 - 8)) and a u (1 - 8)/(1 + X(1 - 8)).
These equations have a natural interpretation. When X increases
(meaning B puts more weight on the social good and less
on his own material payoffs), both p and a increase. When 8
increases (so that B puts relatively more weight on the maximin
component and less on total surplus), then p increases and a
decreases. That is, both parameters move in the direction of more
concern for the person who has a lower payoff, whether this is A
or B. Indeed, looking at p/u = 1/(1 - 8) makes this even clearer.
Increasing p and a by the same proportion indicates a decrease in
self-interestedness, X, whereas increasing the ratio indicates an
increase in 8.
Before defining the full model that incorporates reciprocity,
we first define an equilibrium notion based just on these socialwelfare
preferences. To put preferences in the context of games,
let Ai by Player i's pure strategies, S, be Player i's mixed strategies,
and Si xjiSj be the set of strategies for all players
besides Player i. The material payoffs are determined by actions
taken, where 7ri(al, . . . , aN) represents Player i's payoffs given
actions (a1, . . . , aN).
DEFINITION. For given parameters (N,6) E [0,1], a social-welfare
equilibrium (SWE) of the material game (A1, . .
AN; IT, . . . , ITN) is a strategy profile (s, . . . , SN) that
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UNDERSTANDING SOCIAL PREFERENCES 853
corresponds to Nash equilibrium of the game (A1, . . .
Vj(rr), . . . , VN('r)), where Vi(ur) is Player i's (Xh,)-s
welfare utility function.
Because r1, . .. , ar are continuous in the players' acti
the functions Vi(ir) are well-defined and continuous in the p
ers' actions, a SWE always exists. In both reciprocity-free
ronments, where players are unlikely to be motivated by rec
ity, and in "simple-model environments," where researchers
the most tractable model possible, SWE can provide mor
planatory power than other distributional models.46 Bu
also serves as a foundation for our reciprocity model. In
with an important restriction placed on the parameters o
model, every SWE will be an equilibrium in our full recip
model.
To begin to incorporate reciprocity, consider a strategy profile
s - (s1,S2, . . . , S,), as well as a demerit profile, d = (d,, .
dn), where dk E [0,1] for all k. Below, d will be determinedendogenously. For now, dk can be interpreted roughly as a measure
of how much Player k deserves, where the higher the value
of dk, the less others think Player k deserves. With this interpretation,
we define players' preferences as a function of both their
underlying social-welfare preferences and how they feel about
other players:
U,(s,d) (1 - X) n-, + X [. - min [Ir,, minm, {(rrm + bdm}]
+ (1 - ws) 4r, + L max [1 - kdm,O]Trm -f dmnTrm ,
where b, k, and f are nonnegative parameters of the model. The
key new aspect to these preferences is that the greater is dj forj f
i, the less weight Player i places on Playerj's payoff. Hence, these
preferences say that the more Player i feels that a Player j is
being a jerk, the less Player i wants to help him. When the
parameter f is positive, Player i may in fact wish to hurt Player
j when Player j is being a jerk. The nature of these preferences
46. As with other distributional models, one could readily define a range of
solution concepts with respect to social-welfare preferences. Both refinements of
Nash equilibrium (such as subgame-perfect Nash equilibrium) and less restrictive
concepts (such as rationalizability) can be applied directly to the transformed
games.
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854 QUARTERLY JOURNAL OF ECONOMICS
can be seen most starkly by setting f = 0 and assuming that b
and k are very large. Then the preferences Ui(s,d) imply that
Player i maximizes the disinterested social-welfare-maximizing
allocation among all those other players for which dj = 0-that
is, among all the deserving others-and ignores the payoffs
among those who are undeserving.
We begin endogenizing the demerits d by defining, for every
profile of strategies si and demerits d-i for other players, and
every g E [0,1], the set of Player i's strategies that would
maximize her utility if she put weight g on the social good and
weight 1 - g on her own payoff:
S*(s-,,d_,;g) fs, ES, s, E argmax (1 - g)?r,
+ g 8 min [,rr, minm,l {ITm + bdm}l
+ (1 - )L .nT j- k dm'TmT - fm dm 1mT ,n M.f i M:A
where -r is the profile of material payoffs. "Typically,"
S*(si,d_i,g) will be a singleton set. The material payoffs are afunction of players' actions, and hence strategies; we suppress
this fact in our notation.
We let gi(s,d) be some upper hemi-continuous and convexvalued
correspondence from (s,d) into the set [0,1] such that
gi(s,d) {glsi E S((s_ ,d _,g)}.47 The function gi(s,d) will serve
as a measure of how appropriately other players feel that Player
i is behaving when they determine how to reciprocate. It can be
interpreted as the degree to which Player i is pursuing the social
47. More exactly, for values (s,d) where (gIs' E ST(s',,d' ,,g)) is nonempty
for all (s',d') in a large-enough neighborhood of (s,d), then g,(s,d) = {gIs, E
S*(s_,,di,g)). The full definition of g,(s,d) is as follows. Let e(s,d) be theneighborhood around (s,d) with all components within E > 0 of (s,p). We then let
g,(s,d) be any upper hemi-continuous and convex-valued correspondence such
that {g s, E S*(s_,,d_,,g)} C g,(s,d) C G(E,s,d), where G(e,s,d) is the convex
hull of {g t, C S*(t_,,,_,,g) for some (t,X) CE (s,d)l if {gIt- C S*(t_,,X,g) for
some (t,X) E E(s,d)) is nonempty, and G(E,s,d) = [0,11 if {(gt, E S t_,,X_,,g) for
some (t,y) C E(s,d)} is empty. This is entirely unrestrictive when (gtt, E
S*(t_,,X_y,g) for some (t,X) CE (s,d)) is empty. But, assuming as we do that E is
small, g,(s,d) - {gls, E S*(s-,,d_,,g)) when {(gs, C S*(s_,,d_,,g)) is nonempty.
This convoluted formulation embeds a "smoothing" procedure that is a common
trick to assure continuity in reciprocity models (see, e.g., Rabin [1993] and Falk
and Fischbacher [1998]), assuring here that there exists such a correspondence
meeting the criteria of upper hemi-continuity and convexity.
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UNDERSTANDING SOCIAL PREFERENCES 855
good (that is, pursuing the disinterested social-welfare cri
by choosing si in response to s -i, given that she has di
d_i toward the other players. Except for a technical fix t
that gi(s,d) is upper hemi-continuous and convex-valu
interpretation holds when there exists some degree of con
the social good that, combined with self-interest, can
Player i's choice. But some strategies may not be consisten
any such weighting-as, for instance, when a person c
Pareto-inefficient allocation even when all other player
having well. In such cases, our model does not pin dow
ticular functional form, and hence is quite unrestrictive.
The unrestrictiveness of our model in such cases is par
technical convenience and because it does not matter much
we do not restrict gi(s,d) when {(gsi E S*(si,di,g)) ialso because we do not feel we know the right psychology
people interpret seemingly unmotivated Pareto-damaging
ior or behavior that seems motivated by different norms
ness than expected.
To derive demerit profiles from these functions, we assu
other players compare each gi(s,d) with some selflessness
X*-the weight they feel a decent person should put on so
fare. Specifically, we assume that other players' level of a
toward Player i corresponds to ri(s,d,X*) E {min [g - X
gi(s,d)). That is, whenever max {g g E gi(s,d)) < X*, Play
generate some degree of animosity in others, since he is jud
hurting others relative to what they would get if he were
social-welfare preferences with X - */. When min {g g E
X*, others will feel no animosity toward Player i. Requiring
of ri(s,d,X*) to be nonnegative greatly simplifies the mod
however, also a substantive assumption that essentially
positive reciprocity. But given the lack of positive reciproci
data and those of others, it may not be a costly restriction
situations. We can now define our solution concept.
DEFINITION. The strategy profile s is a reciprocal-fairness
rium (RFE) with respect to parameter profiles , K*,
f and correspondence gi(s,d) if there exists d where, fo
there exists gi E gi(s,d) such that
1) si E argmax Ui(s,d), and
2) di = max [K,* - gi,0].
48. It would be more problematic if we were to use it to predict n
rium outcomes, or outcomes for heterogeneous preferences.
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856 QUARTERLY JOURNAL OF ECONOMICS
A strategy profile is a RFE if every player is maximizing her
expected utility given other players' strategies and given some
demerit profile that is itself consistent with the profile of strategies.
While not stated in that framework, this definition implicitly
corresponds to a psychological Nash equilibrium of a psychological
game as formulated by Geanakoplos, Pearce, and Stacchetti
[1989]. If we were to define a nonequilibrium notion of players'
preferences, the entire formal apparatus would be needed. Because
we just define the equilibrium concept, suppressing the
psychological-game apparatus is both feasible and tractable.49
The implications of RFE depend, of course, on the specific
parameter values assumed, and hence it is unrestrictive insofar
as there are many degrees of freedom in interpreting behavior as
consistent with RFE. But two results enhance the applicability of
reciprocal-fairness equilibrium.
THEOREM 1. For all parameter values and for all games, the set of
RFE is nonempty.
Proof. Let h be the mapping from (s,d) into itself defined by
the best-response correspondences si argmax Ui(s,d) and the
demerit functions di(s,d) E {rl3 g E gi(s,d) such that r = max
[X* - g,0]}). If this mapping is upper hemi-continuous and
convex-valued, then it will have a fixed point, and this fixed point
will be a RFE. By the continuity of Ui(s,d) and the expectedutility
structure, argmax Ui(s,d) is upper hemi-continuous and
convex-valued. The component di(s,d) is upper hemi-continuous
and convex-valued because gi(s,d) is, by assumption, upper hemi-
49. Our model does not incorporate any sophisticated notion of sequential
rationality, as have some recent reciprocity models, such as Dufwenberg and
Kirchsteiger [1998] and Falk and Fischbacher [1998]. We do not do so, partly to
keep our model simple, and partly because some of the better predictions made by
these models are obtained in our model as well without sequential refinements, by
assuming that players are motivated to help others even in the absence of sacrifice
by others. Moreover, we suspect that much of the intuition in these models-and
the evidence invoked in favor of these intuitions--derive from heterogeneous and
nonequilibrium play in experiments, rather than from a notion of how players
should behave at points in a game that really are "off the equilibrium path." If it
is unrealistic to assume that the second mover in a sequential prisoner's dilemma
will play a strategy of unconditional cooperation no matter what a first mover
does, it is probably not because unconditional cooperation is not a best response to
certainty that the first mover will cooperate. It seems more likely that the real
positive probability (due either to heterogeneous preferences or disequilibrium)
that a first mover will defect induces the second mover to defect in response to an
interpretable on-the-equilibrium-path play by the first mover, rather than as part
of an off-the-equilibrium-path strategy.
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UNDERSTANDING SOCIAL PREFERENCES 857
continuous and convex-valued. Hence, h is upper hemi-con
ous and convex-valued, proving the theorem.
Existence clearly enhances the applicability of the solu
concept. A second feature also enhances the applicability o
model despite potential complications due to incorporating
procity. Above, we noted that social-welfare equilibria would
a prominent role in our model. Because of the reciprocity co
nent in preferences (operative when dk > 0 for some k), reci
cal-fairness equilibria might not correspond to social-we
equilibria. Outcomes such as noncooperation in the priso
dilemma can be "concern-withdrawal equilibria." Indeed, if
ers hold each other to very high standards of selflessness-if
very high-it may be that such negative outcomes are the
RFE. But if all players' intrinsic desire X to pursue the social
rather than self-interest is at least as great as the standard X
which people hold each other, then all social-welfare equi
will be reciprocal-fairness equilibria.
THEOREM 2. For all vectors of parameters such that X* - X,
social-welfare equilibrium is a reciprocal-fairness equilibr
Proof. Consider a SWE s*. Each Player i is playing a b
response given di = 0, so that X E gi(s,d). If X - X*, thisthat 0 = max [X* - X,0]. Hence, s* is a RFE with respect t
demerit profile d = 0.
Theorem 2 indicates that SWE may serve as a good heu
to predict the types of "cooperative" equilibria that can occu
course, there may additionally be negative equilibria, and
importantly for interpreting experimental data) there m
either disequilibrium play or heterogeneous preferences,
X < X* for some of the participants, so that some bad beh
and corresponding retaliation, may be observed.
Despite the unrestrictiveness of reciprocal-fairness equ
rium in some ways, it is clearly too restrictive in other respe
is too restrictive to be directly applied to experimental evide
on the other hand, because it does not allow for other soc
preferences, heterogeneity in players' preferences, or noneq
rium play. And the model clearly omits patterns of behavior
seem apparent in the data, such as complicity effects. By ass
ing homogeneous preferences, it rules out even a minor
subjects being motivated by preferences such as difference a
sion. We think any prospects for good-fitting models will ev
ally have to account better for such heterogeneity than w
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858 QUARTERLY JOURNAL OF ECONOMICS
done in this paper. We can also think of specific examples-such
as Barc5, where we seem to observe no negative reciprocity (when
compared with Berk29, say) even when it is free-that, if they
turn out to be consistent patterns, would raise problems for this
model.
APPENDIX 2: SAMPLE INSTRUCTIONS
INSTRUCTIONS
Thank you for participating in this experiment. You w
receive $5 for your participation, in addition to other money
paid as a result of decisions made in the experiment.
You will make decisions in several different situations
("games"). Each decision (and outcome) is independent from e
of your other decisions, so that your decisions and outcomes
one game will not affect your outcomes in any other game.
In every case, you will be anonymously paired with one (
more) other people, so that your decision may affect the payoffs
others, just as the decisions of the other people in your group m
affect your payoffs. For every decision task, you will be pai
with a different person or persons than in previous decisions.
There are "roles" in each game-generally A or B, althou
some games also have a C role. If a game has multiple decisio
(some games only have decisions for one role), these decisions w
be made sequentially, in alphabetical order: "A" players wil
complete their decision sheets first, and their decision sheets w
then be collected. Next, "B" players complete their decision shee
and these will be collected. Etc.
When you have made a decision, please turn your decision
sheet over, so that we will know when people have finished.
There will be two "periods" in each game, and so you will play
each game twice, with a different role (and a different anonymous
pairing) in each case. You will not be informed of the results of
any previous period or game prior to making your decision.
Although you will thus have 8 "outcomes" from the games
played, only two of these outcomes will be selected for payoffs. An
8-sided die will be rolled twice at the end of the experiment and
the (different) numbers rolled will determine which outcomes
(1-8) are used for payoffs.
At the end of the session, you will be given a receipt form to
be filled out, and you will be paid individually and privately.
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UNDERSTANDING SOCIAL PREFERENCES 859
Please feel free to ask questions at any point if you fe
need clarification. Please do so by raising your hand. P
NOT attempt to communicate with any other participants
session until the session is concluded.
We will proceed to the decisions once the instructions are
clear. Are there any questions?
PERIOD 1
GAME 3
In this period, you are person A.
You have no choice in this game. Player B's choice determines
the outcome. If player B chooses Bi, you would receive 800,
and player B would receive 200. If player B chooses B2, you would
each receive 0.
B
A
B1 / \ B2
A 800 0 A
B 200 0 B
DECISION
I understand I have no choice in this game
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860 QUARTERLY JOURNAL OF ECONOMICS
PERIOD 1
GAME 3
In this period, you are person B.
You may choose B1 or B2. Player A has no choice in this
game. If you choose B1, you would receive 200 and player A would
receive 800. If you choose B2, you would each receive 0.
B
A
BI \B2B1 / \ B2
A 800 0 A
B 200 0 B
DECISION
I choose: B1 B2
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UNDERSTANDING SOCIAL PREFERENCES 861
PERIOD 1
GAME 1
In this period, you are person A.
You may choose Al or A2. If you choose Al, you would receive
750, and player B would receive 0. If you choose A2, then player
B's choice of B1 or B2 would determine the outcome. If you choose
A2 and player B chooses B1, you would each receive 400. If you
choose A2 and player B chooses B2, you would receive 750, and he
or she would receive 375. Player B will make a choice without
being informed of your decision. Player B knows that his or her
choice only affects the outcome if you choose A2, so that he or she
will choose B1 or B2 on the assumption that you have chosen A2
over Al.
A
A
Al / \ A2
A 750
B O
B
A
B1 / \ B2
A 400 750 A
B 400 375 B
DECISION
I choose: Al A2
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862 QUARTERLY JOURNAL OF ECONOMICS
PERIOD 1
GAME 1
In this period, you are person B.
You may choose B1 or B2. Player A has already made a
choice. If he or she has chosen Al, he or she would receive 750,
and you would receive 0. Your decision only affects the outcome if
player A has chosen A2. Thus, you should choose B1 or B2 on the
assumption that player A has chosen A2 over Al. If player A has
chosen A2 and you choose B1, you would each receive 400. If
player A has chosen A2 and you choose B2, then player A would
receive 750, and you would receive 375.
A
A
Al / \ A2
/ \
A 750
B O
B
A
BI / \ B2
A 400 750 A
B 400 375 B
DECISION
I choose: Al A2
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UNDERSTANDING SOCIAL PREFERENCES 863
APPENDIX 3: ROLE REVERSAL
The role-reversal data for each of the 19 games are
below. The (two-tailed) p-value used reflects the perce
time that a difference in rates as large as the one observe
occur randomly.
For each type of behavior as A, if if
did the person help A as B? Out Enter p-value
Helping A doesn't affect B's payoff
Barc5 (36) A chooses (550,550) or lets B choose 5/14 19/22 .00
(400,400) vs. (750,400)
Barc7 (36) A chooses (750,0) or lets B choose 15/17 19/19 .12
(400,400) vs. (750,400)
Berk28 (32) A chooses (100,1000) or lets B choose 10/16 11/16 .73
(75,125) vs. (125,125)
Berk32 (26) A chooses (450,900) or lets B choose 16/22 1/4 .06
(200,400) vs. (400,400)
Helping A is costly to B
Barc3 (42) A chooses (725,0) or lets B choose 10/31 6/11 .19
(400,400) vs. (750,375)
Barc4 (42) A chooses (800,0) or lets B choose 11/35 5/7 .05
(400,400) vs. (750,375)
Berk21 (36) A chooses (750,0) or lets B choose 3/17 11/19 .01
(400,400) vs. (750,375)
Barc6 (36) A chooses (750,100) or lets B choose 8/33 1/3 .73
(300,600) vs. (700,500)
Barc9 (36) A chooses (450,0) or lets B choose 2/25 0/11 .24
(350,450) vs. (450,350)
Berk25 (32) A chooses (450,0) or lets B choose 3/20 3/12 .48
(350,450) vs. (450,350)
Berkl9 (32) A chooses (700,200) or lets B choose 13/18 12/14 .36
(200,700) vs. (600,600)
Berkl4 (22) A chooses (800,0) or lets B choose 6/15 6/7 .05
(0,800) vs. (400,400)
Barcl (44) A chooses (550,550) or lets B choose 1/42 2/2 .00
(400,400) vs. (750,375)
Berkl3 (22) A chooses (550,550) or lets B choose 1/19 3/3 .00
(400,400) vs. (750,375)
Berkl8 (32) A chooses (0,800) or lets B choose 0/0 14/32
(0,800) vs. (400,400)
Helping A is beneficial to B
Barcll (35) A chooses (375,1000) or lets B choose 15/19 16/16 .05
(350,350) vs. (400,400)
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864 QUARTERLY JOURNAL OF ECONOMICS
APPENDIX 3 (CONTINUED)
For each type of behavior as A, if if
did the person help A as B? Out Enter p-value
Berk22 (36) A chooses (375,1000) or lets B choose 13/14 22/22 .20
(250,350) vs. (400,400)
Berk27 (32) A chooses (500,500) or lets B choose 11/13 18/19 .34
(0,0) vs. (800,200)
Berk31 (26) A chooses (750,750) or lets B choose 16/19 7/7 .26
(0,0) vs. (800,200)
Berk30 (26) A chooses (400,1200) or lets B choose 19/20 4/6 .06
(0,0) vs. (400,200)
APPENDIX 4: GAME-BY-GAME CONSISTENCY
WITH DISTRIBUTIONAL MODELS
In this table we allow A to have any beliefs about B's response
to Enter. Entries in the following tables indicate which models, C
(competitive preferences), D (difference aversion), Q (social-welfare
preferences), and $ (self-interest) each move is consistent with.
B plays B plays
A Exit A Enter Left Right
Game N Prefs. N Prefs. N Prefs. N Prefs.
1 A(550,550);
B(400,400)-(750,375) 42 C,D,Q,$ 2 C,D,Q,$ 41 C,D,Q,$ 3 Q
2 B(400,400)-(750,375) - - 25 C,D,Q,$ 23 Q
3 A(725,0);
B(400,400)-(750,375) 31 C,D,Q,$ 11 C,D,Q,$ 26 C,D,Q,$ 16 Q
4 A(800,0);
B(400,400)-(750,375) 35 C,D,Q,$ 7 D,Q 26 C,D,Q,$ 16 Q
5 A(550,550);
B(400,400)-(750,400) 18 C,D,Q,$ 28 C,D,Q,$ 15 C,D,$ 31 Q,$
6 A(750,100);
B(300,600)-(700,500) 33 C,D,Q,$ 3 D,Q 27 C,D,Q,$ 9 D,Q
7 A(750,0);
B(400,400)-(750,400) 17 C,D,Q,$ 19 D,Q,$ 2 C,D,$ 34 Q,$
8 B(300,600)-(700,500) - - 24 C,D,Q,$ 12 D,Q
9 A(450,0);
B(350,450)-(450,350) 25 C,D,Q,$ 11 D,Q,$ 34 C,D,Q,$ 2
11 A(375,1000);
B(400,400)-(350,350) 19 C,D,Q,$ 16 C,D,Q,$ 31 C,D,Q,$ 4
13 A(550,550);
B(400,400)-(750,375) 19 C,D,Q,$ 3 C,D,Q,$ 18 C,D,Q,$ 4 Q
14 A(800,0); B(0,800)(400,400)
15 C,D,Q,$ 7 D,Q 10 C,D,Q,$ 12 D,Q
15 B(200,700)-(600,600) - - 6 C,D,Q,$ 16 D,Q
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UNDERSTANDING SOCIAL PREFERENCES 865
APPENDIX 4 (CONTINUED)
B plays B plays
A Exit A Enter Left Right
Game N Prefs. N Prefs. N Prefs. N Prefs.
17 B(400,400)-(750,375) - - 16 C,D,Q,$ 16 Q
18 A(0,800); B(0,800)(400,400)
0 32 C,D,Q,$ 14 C,D,Q,$ 18 D,Q
19 A(700,200);
B(200,700)-(600,600) 18 C,D,Q,$ 14 D,Q 7 C,D,Q,$ 25 D,Q
21 A(750,0);
B(400,400)-(750,375) 17 C,D,Q,$ 19 D,Q,$ 22 C,D,Q,$ 14 Q
22 A(375,1000);
B(400,400)-(250,350) 14 C,D,Q,$ 22 C,D,Q,$ 35 C,D,Q,$ 1 C
23 B(800,200)-(0,0) - - 36 C,D,Q,$ 0 C,D
25 A(450,0);
B(350,450)-(450,350) 20 C,D,Q,$ 12 D,Q,$ 26 C,D,Q,$ 6
26 B(0,800)-(400,400) - - 25 C,D,Q,$ 7 D,Q
27 A(500,500);
B(800,200)-(0,0) 13 C,D,Q,$ 19 C,D,Q,$ 29 C,D,Q,$ 3 C,D
28 A(100,1000);
B(75,125)-(125,125) 16 C,D,Q,$ 16 C,D,Q,$ 11 C,D,$ 21 Q,$
29 B(400,400)-(750,400) - - 8 C,D,$ 18 Q,$
30 A(400,1200);
B(400,200)-(0,0) 20 C,D,Q,$ 6 C,D,$ 23 C,D,Q,$ 3 C,D
31 A(750,750);
B(800,200)-(0,0) 19 C,D,Q,$ 7 C,D,Q,$ 23 C,D,Q,$ 3 C,D
32 A(450,900);
B(200,400)-(400,400) 22 C,D,Q,$ 4 C,D 9 C,$ 17 D,Q,$
Total A choices = 671 C = 579 D = 671 Q = 661 $ = 636.
Total B choices = 903 C = 579 D = 685 Q = 836 $ = 690
In this table we assume A correctly assesses actual B play
when choosing.
B plays B plays
A Exit A Enter Left Right
Game N Prefs. N Prefs. N Prefs. N Prefs.
1 A(550,550);
B(400,400)-(750,375) 42 C,D,Q,$ 2 C 41 C,D,Q,$ 3 Q
2 B(400,400)-(750,375) - - 25 C,D,Q,$ 23 Q
3 A(725,0); B(400,400)(750,375)
31 C,D,Q,$ 11 D,Q 26 C,D,Q,$ 16 Q
4 A(800,0); B(400,400)(750,375)
35 C,D,Q,$ 7 D,Q 26 C,D,Q,$ 16 Q
5 A(550,550);
B(400,400)-(750,400) 18 D,Q 28 C,D,Q,$ 15 C,D,$ 31 Q,$
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866 QUARTERLY JOURNAL OF ECONOMICS
APPENDIX 4 (CONTINUED)
B plays B plays
A Exit A Enter Left Right
Game N Prefs. N Prefs. N Prefs. N Prefs.
6 A(750,100);
B(300,600)-(700,500) 33 C,D,Q,$ 3 D,Q 27 C,D,Q,$ 9 D,Q
7 A(750,0); B(400,400)(750,400)
17 C,D,Q,$ 19 D,Q 2 C,D,$ 34 Q,$
8 B(300,600)-(700,500) - - 24 C,D,Q,$ 12 D,Q
9 A(450,0); B(350,450)(450,350)
25 C,D,Q,$ 11 D,Q 34 C,D,Q,$ 2
11 A(375,1000);
B(400,400)-(350,350) 19 Q 16 C,D,Q,$ 31 C,D,Q,$ 4
13 A(550,550);
B(400,400)-(750,375) 19 C,D,Q,$ 3 C 18 C,D,Q,$ 4 Q
14 A(800,0); B(0,800)(400,400)
15 C,D,Q,$ 7 Q 10 C,D,Q,$ 12 D,Q
15 B(200,700)-(600,600) - - 6 C,D,Q,$ 16 D,Q
17 B(400,400)-(750,375) - - 16 C,D,Q,$ 16 Q
18 A(0,800); B(0,800)(400,400)
0 32 C,D,Q,$ 14 C,D,Q,$ 18 D,Q
19 A(700,200);
B(200,700)-(600,600) 18 C,D,Q,$ 14 D,Q 7 C,D,Q,$ 25 D,Q
21 A(750,0);
B(400,400)-(750,375) 17 C,D,Q,$ 19 D,Q 22 C,D,Q,$ 14 Q
22 A(375,1000);
B(400,400)-(250,350) 14 Q 22 C,D,Q,$ 35 C,D,Q,$ 1 C
23 B(800,200)-(0,0) - - 36 C,D,Q,$ 0 C,D
25 A(450,0);
B(350,450)-(450,350) 20 C,D,Q,$ 12 D,Q 26 C,D,Q,$ 6
26 B(0,800)-(400,400) - - 25 C,D,Q,$ 7 D,Q
27 A(500,500);
B(800,200)-(0,0) 13 D,Q 19 C,D,Q,$ 29 C,D,Q,$ 3 C,D
28 A(100,1000);
B(75,125)-(125,125) 16 Q 16 C,D,Q,$ 11 C,D,$ 21 Q,$
29 B(400,400)-(750,400) - - 8 C,D,$ 18 Q,$
30 A(400,1200);
B(400,200)-(0,0) 20 C,D,Q,$ 6 C,D 23 C,D,Q,$ 3 C,D
31 A(750,750);
B(800,200)-(0,0) 19 C,D,Q,$ 7 C 23 C,D,Q,$ 3 C,D
32 A(450,900);
B(200,400)-(400,400) 22 C,D,Q,$ 4 C,D 9 C,$ 17 D,Q,$
Total A choices = 671 C = 579 D = 671 Q = 661 $ = 636.
Total B choices = 903 C = 579 D = 685 Q = 836 $ = 690.
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UNDERSTANDING SOCIAL PREFERENCES 867
APPENDIX 5: FIRST-MOVER BEHAVIOR
Table 3.1: A's sacrifice helps B Maximize Sacrifice
Barc5 (36) A chooses (634,400) or (550,550) .61 .39
Barc7 (36) A chooses (750,0) or (729,400) .47 .53
Berk28 (32) A chooses (108,125) or (100,1000) .50 .50
Barc3 (42) A chooses (725,0) or (533,390) .74 .26
Barc4 (42) A chooses (800,0) or (533,390) .83 .17
Berk21 (36) A chooses (750,0) or (536,390) .47 .53
Barc6 (36) A chooses (750,100) or (400,575) .92 .08
Barc9 (36) A chooses (450,0) or (356,444) .69 .31
Berk25 (32) A chooses (450,0) or (369,431) .62 .38
Berkl9 (32) A chooses (700,200) or (512,622) .56 .44
Berkl4 (22) A chooses (800,0) or (216,584) .68 .32
Berkl8 (32) A chooses (224,576) or (0,800) 1.00 .00
Barcll (35) A chooses (394,394) or (375,1000) .46 .54
Berk22 (36) A chooses (396,398) or (375,1000) .61 .39
Berk27 (32) A chooses (728,182) or (500,500) .59 .41
Table 3.2: A's sacrifice hurts B Maximize Sacrifice
Berk32 (26) A chooses (450,900) or (330,400) .85 .15
Barcl (44) A chooses (550,550) or (424,398) .96 .04
Berkl3 (22) A chooses (550,550) or (463,396) .86 .14
Berk31 (26) A chooses (750,750) or (704,176) .73 .27
Berk30 (26) A chooses (400,1200) or (352,176) .77 .23
DEPARTMENT OF ECONOMICS, UNIVERSITY OF CALIFORNIA, SANTA BARB
DEPARTMENT OF ECONOMICS, UNIVERSITY OF CALIFORNIA, BERKELEY
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