Games and Economic Behavior 62 (2008) 287–303
www.elsevier.com/locate/geb
Testing theories of fairness—Intentions matter
Armin Falk a,b,1
, Ernst Fehr c,2
, Urs Fischbacher c,∗
a IZA, Bonn, Germany
b University of Bonn, Bonn, Germany
c University of Zurich, Zurich, Switzerland
Received 23 July 2003
Available online 16 June 2007
Abstract
Recently developed models of fairness can explain a wide variety of seemingly contradictory facts. One
of the most controversial and yet unresolved issues in the modeling of fairness preferences concerns the
behavioral relevance of fairness intentions. Intuitively, fairness intentions seem to play an important role in
economic relations, political struggles, and legal disputes but there is surprisingly little direct evidence for
its behavioral importance. We provide experimental evidence for the behavioral relevance of fairness intentions
in this paper. Our main result indicates that the attribution of fairness intentions is important in both
the domains of negatively and positively reciprocal behavior. This means that equity models exclusively
based on preferences over the distribution of material payoffs cannot capture reciprocal behavior. Models
that take players’ fairness intentions and distributional preferences into account are consistent with our data,
while models that focus exclusively on intentions or on the distribution of material payoffs are not.
© 2007 Elsevier Inc. All rights reserved.
JEL classification: D63; C78; C91
Keywords: Fairness; Reciprocity; Intentions; Experiments; Moonlighting game
* Corresponding author at: Institute for Empirical Research in Economics, Blümlisalpstrasse 10, CH-8006 Zurich,
Switzerland.
E-mail addresses: falk@iza.org (A. Falk), efehr@iew.uzh.ch (E. Fehr), fiba@iew.uzh.ch (U. Fischbacher).
1 Postal address: Institute for the Study of Labor and University of Bonn, Schaumburg-Lippe Strasse 7/9, 53113 Bonn,
Germany.
2 Postal address: Institute for Empirical Research in Economics, Blümlisalpstrasse 10, CH-8006 Zurich, Switzerland.
0899-8256/$ – see front matter © 2007 Elsevier Inc. All rights reserved.
doi:10.1016/j.geb.2007.06.001
288 A. Falk et al. / Games and Economic Behavior 62 (2008) 287–303
1. Introduction
A considerable body of evidence indicates that concerns for fairness and reciprocity motivate
a substantial number of people. Moreover, the presence of fair-minded people is likely to have
important economic effects (Kahneman et al., 1986; Camerer and Thaler, 1995; Bewley, 1999;
Fehr and Gächter, 2000). This has led to the development of several fairness models (Rabin,
1993; Levine, 1998; Dufwenberg and Kirchsteiger, 2004; Falk and Fischbacher, 2006; Fehr and
Schmidt, 1999; Bolton and Ockenfels, 2000; Charness and Rabin, 2002). These models share
the property that some people are assumed to have a preference for fairness—in addition to their
preference for material payoffs. The impressive feature of these models is that they are capable
of predicting a wide variety of seemingly contradictory facts correctly.
This paper examines the most controversial question in the modeling of fairness preferences:
the role of fairness intentions.3 Do fair-minded people respond to fair or unfair intentions, or
do they respond solely to fair or unfair outcomes? One class of fairness models—the inequity
aversion models of Fehr and Schmidt (1999) and Bolton and Ockenfels (2000)—is based on
the assumption that fairness intentions are behaviorally irrelevant. Another class of models (e.g.,
Rabin, 1993; Falk and Fischbacher, 2006; Dufwenberg and Kirchsteiger, 2004) assigns fairness
intentions a major behavioral role.
The answer to our question is of great practical and theoretical interest. At the theoretical level,
the question not only concerns the proper modeling of fairness preferences, but also standard
utility theory as well. Standard utility theory assumes that the utility of an action depends solely
on its consequences and not on the intention behind the action. Therefore, if the attribution of
intentions turns out to be behaviorally important, the “consequentialism” inherent in standard
utility models is also in doubt. The issue is important at the practical level because many relevant
decisions are likely to be affected if the attribution of intentions matters. Fairness attributions
are likely to influence decision-making in firms and other organizations as well as in markets
and the political arena. Political decisions and business decisions, for instance, often affect some
parties’ material payoffs negatively. If the response of the negatively affected parties also takes
the decision-maker’s fairness intentions into account, it will be much easier to prevent opposition
when the decision-maker can credibly claim that he is somehow forced—by law, by international
competition, or by some other external force—to take the action. It is, therefore, no coincidence
that the rhetoric of politicians and business leaders often appeals to the phrase that “there is no
alternative”. If there is indeed no alternative, it is not possible to attribute unfair intentions to
the action because the decision-maker cannot be held responsible for the action. If, in contrast,
obvious alternative actions are available, it is much easier for the affected parties to attribute
unfair intentions to the action and, as a consequence, their opposition will be much stronger.
The attribution of intentions is also important in law (Huang, 2000). Intentions often distinguish
between whether the same action is a tort or a crime and whether a tort should involve
punitive damages. Other distinctions made in criminal law concern whether an action is taken
purposely, knowingly, recklessly, or negligently (see Model Penal Code §2.02(1)–(2)). Thus,
the penal code (which represents a codified broad sense of justice) distinguishes quite carefully
between the consequences of an action and its underlying intentions.
Gouldner (1960) points out the importance of intentions in his classic account of reciprocity
by conjecturing that the force of reciprocity depends on the motives imputed to the donor and
3 This paper suffered from serious editorial delays at different journals. An early version of our results can be found in
Falk et al. (2000).
A. Falk et al. / Games and Economic Behavior 62 (2008) 287–303 289
the donor’s own free will. Although this notion of reciprocity is highly suggestive, providing
direct and unambiguous evidence for the behavioral relevance of fairness intentions has proven
very difficult up to now. This is not surprising with regard to field data because outcomes and
intentions are usually inextricably intertwined in the field. Yet, the issue has been quite elusive,
even in laboratory experiments. Charness (2004), Bolton et al. (1998), Offerman (2002) and Cox
(2004) find little or no evidence that the attribution of fairness intentions matters in the domain
of positively reciprocal behavior.4 Blount (1995) and Offerman (2002) find evidence that it matters
in the domain of negatively reciprocal behavior but, as we will argue below, these studies
have some methodological problems. Thus, we face the puzzle that, intuitively, the attribution of
fairness intentions seems to be important while, the issue remains controversial in light of the
prevailing evidence.
We provide experimental evidence for the behavioral relevance of fairness attributions in
this paper. Our main result is that the attribution of fairness intentions is important in both
the domains of negatively and positively reciprocal behavior. When the experimental design
rules out the attribution of fairness intentions, reciprocal responses are substantially weaker.
This result is corroborated both at the individual as well as at the aggregate level. Not only
do some individuals show weaker reciprocal responses when it is impossible to attribute fairness
intentions; a non-negligible fraction of the subjects (30 percent) exhibit no reciprocal
behavior when fairness attributions are ruled out, i.e., they behave like selfish individuals. However,
when the design allows for the attribution of fairness intentions, no subject behaves in
a fully selfish manner. This indicates that the recently developed inequity aversion models of
Fehr and Schmidt (1999) and Bolton and Ockenfels (2000) are incomplete because they neglect
fairness intentions. The behavioral relevance of fairness intentions does, of course, not rule
out that subjects also respond to unfair outcomes. Our results indicate that, on average, subjects
exhibit weakly reciprocal behavior even if they cannot attribute fairness intentions. Thus,
models that are exclusively based on intention-driven reciprocal behavior (e.g., Rabin, 1993;
Dufwenberg and Kirchsteiger, 2004) are also incomplete. Models that combine both aspects
(like e.g. Falk and Fischbacher, 2006) fit our data best.
Our experimental design also provides an opportunity for examining the extent to which the
same individuals exhibit both positive and negative reciprocity. To our knowledge, no study
examines whether positive and negative reciprocity is correlated at the level of the individual.
Previous studies can only answer the question whether a given individual exhibits a positively
or a negatively reciprocal response. It turns out that—when fairness attributions are possible—
40 percent of the subjects exhibit both positively and negatively reciprocal responses. However,
a large fraction of 21 percent exhibit only positively reciprocal responses and 15 percent show
only negatively reciprocal responses.
The paper is organized as follows. The next section discusses potential obstacles in finding
behavioral effects of fairness intentions. Section 3 presents the experimental design. Section 4
discusses the predictions of several fairness theories. Results are presented in Section 5. Section 6
provides a short discussion.
4 Positive reciprocity is defined as a kind response to an action that leads to a fair outcome or is driven by fair intentions.
Negative reciprocity is defined as a hostile response to an action that leads to an unfair outcome or is driven by unfair
intentions. Note that, for convenience, we also call a response to a random event a reciprocal action.
290 A. Falk et al. / Games and Economic Behavior 62 (2008) 287–303
2. Obstacles for finding behavioral effects of fairness intentions
Before presenting our experimental design, we discuss the potential reasons for the lack of
convincing evidence in favor of fairness intentions; four potential reasons exist in our opinion.
The first reason is that a potential confound with the efficiency motive exists in some studies.
Andreoni and Miller (2002), Bolle and Kritikos (2001), Charness and Rabin (2002) and Engelmann
and Strobel (2004) report results suggesting the presence of a non-negligible fraction of
subjects willing to increase efficiency. These subjects seem to be willing to bear some cost in
order to increase the total payoff, i.e., the sum of the payoffs that accrues to all the parties. This
motive could have swamped the positively reciprocal responses in the studies of Charness (2004),
Bolton et al. (1998) and Offerman (2002) because the second mover’s reciprocal behavior was
associated with large efficiency increases in these studies. It is also possible that reciprocity motives
and efficiency motives interact in a yet unknown way. For this reason, our design rules out
an increase in the total payoff due to reciprocal responses.
A second reason is related to the issue of repetition. Subjects faced a different opponent in
each of ten periods in Charness (2004). Repetitions may create all sorts of ill-understood noise
and spillovers across periods that make it difficult to isolate the attribution of fairness intentions.
For this reason we conducted a one-shot experiment without any repetitions.
A third potential reason for the lack of a behavioral impact of fairness intentions could be
that the treatment manipulations were not strong enough. Ideally, two treatments are needed to
isolate the role of fairness intentions, one where first-movers can signal their fairness intentions,
and one where such signals are ruled out completely. The signaling of fairness intentions rests
on two premises:
(i) the first-mover’s choice set actually allows the choice between a fair and an unfair action,
and
(ii) the first-mover’s choice is under the first mover’s full control.
The first premise implies that the treatment manipulation can be “too weak” because the choices
available to the first-mover may not be sufficiently different, i.e., the fairness or unfairness of the
available actions is not salient enough. We solved this problem in our design by giving the firstmover
a choice set that allows for very different actions. In particular, the first-mover could either
increase or decrease the second-mover’s payoff relative to a clearly defined reference point (i.e.,
relative to an initial endowment that was the same for both players). This distinguishes our study
from the studies of Charness (2004), Bolton et al. (1998) and Cox (2004) where the first movers
could only be more or less kind to the second-movers, but they could not hurt them. Perhaps, the
distinction between being more or less kind was not salient enough and, as a consequence, there
was little or no intention-driven reciprocal behavior in these studies.
The fourth reason is related to the second premise above. It concerns the question of how
one can rule out the attribution of fairness intentions to the first mover’s choice. In our view, the
strongest method is to deprive the first mover of any choice at all and to make this salient to
the second mover. We achieved this in our experiment by determining the first mover’s “action”
with a salient random device. Saliency was implemented by rolling dice in front of each second
mover. However, if a random device determines the first mover’s choice, the second movers might
have views about what constitutes fair or unfair random devices. For example, if the random
device determines a very bad outcome for the second mover with high probability, the second
mover may become angry because she views this as a rather unfair device. If, in contrast, human
A. Falk et al. / Games and Economic Behavior 62 (2008) 287–303 291
first movers are unlikely to choose such a bad outcome, the comparison of responses across the
random device and the human choice condition does not isolate the impact of fairness intentions.
The reason is that a confound due to the angry response to an unfair random device is likely to
exist. Our solution to this problem is to implement a random device that mimics the probability
distribution over the actions of human first movers.
A random device determined the first mover’s “action” both in Blount (1995) and Offerman
(2002).5 However, only Blount kept the probability distribution of first mover actions constant
across the random device and the human choice conditions. Although Blount’s study is very
clean and convincing in this regard, it faces other methodological problems. The results of her
ultimatum game may be affected by the fact that subjects in the human choice condition had
to make decisions as a proposer and as a responder before they knew their actual roles. After
subjects had made their decisions in both roles, the role for which they received payments was
determined randomly. This means that the decision situation was not kept constant across the
random device and the human choice condition because the responders also had to put themselves
in the shoes of the proposers in the human choice condition, while this was not the case in the
random device condition.
Deception was involved in one of Blount’s treatments. Subjects believed that there were proposers
although the experimenters actually made the proposals. All subjects in this condition
were “randomly” assigned to the responder role. It could well be that this kind of deception
cannot be hidden from the subjects, i.e., at least a number of subjects might have noticed that
they were deceived. In contrast to this setting, subjects in our experiment knew their role in all
conditions before they made decisions and we had real human subjects in both the first-mover
position and in the second-mover position.
3. Experimental design and procedures
Our experimental design is based on the “moonlighting game” (Abbink et al., 2000). This
game has the advantage that we can examine the impact of fairness intentions on both positively
and negatively reciprocal responses at the individual level. We first describe the moonlighting
game below and then present our two treatments, the Intention treatment and the No-Intention
treatment. Finally, we report the procedures of the experiment.
3.1. The constituent game
The “moonlighting game” is a two-player sequential move game that consists of two stages.
At the beginning of the game, both players are endowed with 12 points. Player A chooses an
action a ∈ {−6,−5,...,5,6} in the first stage. If A chooses a 0, he gives player B a tokens
while if he chooses a < 0, he takes |a| tokens away from B. In case of a 0, the experimenter
triples a so that B receives 3a. If a < 0, A reaps |a| and player B loses |a|. After player B
observes a, she can choose an action b ∈ {−6,−5,...,17,18} at the second stage, where b 0
is a reward and b < 0 is a sanction. A reward transfers b points from B to A. A sanction costs B
exactly |b| but reduces A’s income by 3|b|. Final incomes are determined after B’s decision.
5 Kagel and Wolfe (2001) suggest yet another way for studying the role of intention. They show that—in contrast to the
prediction by inequity aversion models—responders reject offers even though this favors or harms a third party, resulting
in inequity. However, since this third party takes no decision, this inequity is not considered as intentional and is therefore
accepted.
292 A. Falk et al. / Games and Economic Behavior 62 (2008) 287–303
Since As can give and take while Bs can reward or sanction, this game allows for both positively
and negatively reciprocal behavior.
We applied the strategy method in our experiment. This means that player B had to give us
a response for each feasible action of player A, before B was informed about A’s actual choice.
This has several advantages.6 First, it allows us to examine the correlation between positive and
negative reciprocity at the individual level. Thus, we know whether there are subjects who only
exhibit either negatively reciprocal responses or positively reciprocal responses, or whether some
exhibit both types of reciprocity. Second, the strategy method allows us to study the relevance of
intentions for reciprocal behavior at any level of a. This is so because we have sufficiently many
responses to each feasible action of A.
3.2. Treatments
As discussed above, A’s action signals fairness intentions if
(i) A’s choice set allows the choice between saliently fair and saliently unfair decisions, and
(ii) if A’s choice is under his full control.
Our experimental game guarantees condition (i), since it allows A to give or to take different
amounts of money. Condition (ii) is our treatment variable. A himself determines a in the Intention
treatment (I-treatment), thus making him responsible for the consequences of his action; his
action therefore signals intentional kindness (if a is high) or intentional unkindness (if a is low).
In contrast, a random device determines A’s move in the No-intention treatment (NI-treatment).
Consequently, A has no control over his action. His action therefore signals neither good nor bad
intentions.
A’s random move in the NI-treatment was implemented as follows: after B had determined
her strategy, the experimenter went to her place and cast two dice in front of B. Both dice were
ten-sided showing numbers from 0 to 9, i.e., together they created numbers between zero and
99 with equal probability. The number cast was then used to determine A’s move according to
Table 1. For example, if the dice showed a number between 0 and 6, A’s random move was to
take 6 points (a = −6), while if the number was 58, for example, player A’s move was a = 3.
The experimenter entered the respective “choice”. After A’s move had been determined, the
experimenter went to another player B and cast the dice again. This procedure was explained
to Bs in great detail in the instructions.7 Thus, it was completely transparent to each B that
A’s move was determined randomly according to Table 1. Players A also knew that their choice
would be randomly determined but did not know the probability distribution.
6 In principle, the strategy method could induce a different behavior of B relative to a situation where B has to respond
to A’s actual move. In fact, Güth et al. (2001) report an experiment in which they observe behavioral differences between
the strategy method and the specific response method. On the other hand, Brandts and Charness (2000) and Cason and
Mui (1998) report evidence indicating that the strategy method does not induce different behavior. It is important to
note that we used the strategy method in both of our treatments. Therefore, our results are biased only if the impact of
this method differs across treatments. A referee pointed out to us that this could be the case in our experiment: if the
emotional response to an outcome is independent of the method (strategy method or specific response method) when a
person makes the offer, but, subjects only respond emotionally to an (unfair) offer in the case of the random treatment
if they actually experience it, i.e., if the specific response method is used and not the strategy method, then our method
would overestimate the intention effect.
7 The instructions are available at http://www.iew.uzh.ch/home/fischbacher/download/fafefi_test_theories_instr.pdf.
A. Falk et al. / Games and Economic Behavior 62 (2008) 287–303 293
Table 1
Probability distribution of the move of A in the NI-treatment
Realized
number
A’s move a Percent
0–6 −6 7
7–8 −5 2
9–15 −4 7
16–19 −3 4
20–21 −2 2
22–26 −1 5
27–39 0 13
40–46 1 7
47–55 2 9
56–62 3 7
63–73 4 11
74–75 5 2
76–99 6 24
Notice that the randomly determined moves of A according to Table 1 are not equally likely.
For example, a random selection of a = −6 (7 percent chance) is more likely than a = −5
(2 percent chance). Table 1 reflects the actual human decisions of the As who participated in
the moonlighting experiment by Abbink et al. (2000). This table permitted us to approximate a
“human choice distribution” even in the NI-treatment, where choices were random. The choice
distribution given in Table 1 was also presented to Bs in the I-condition, in order to keep everything
constant with the exception of the potential for the attributions of intentions across the NIand
the I-treatments.8 The Bs informed in the I-treatment that the same experiment had already
been conducted and that the relative frequency of As’ decisions in that experiment was identical
to those in Table 1. This was done to induce players B to have the same beliefs about As’ choice
distribution in both treatment conditions. This procedure ruled out the possibility that different
beliefs about the choice distribution of the As affected the Bs’ responses.9 Thus, the two treatments
cannot evoke different fairness judgments with regard to the probability distribution over
the set of feasible actions.10
3.3. Procedure
Before the game started, subjects were randomly assigned to their role as player A or B (in
both treatments). They were seated in front of their terminal and given their instructions. All
subjects had to answer several control questions to ensure the understanding of the experimental
procedures; the experiment did not start until all subjects had answered all questions correctly.
All the players knew both procedures and payoff functions, i.e., they were explained in the instructions
and summarized orally. Losses were possible, and subjects had to cover them with
8 As in the NI-treatment, the players A were not informed about the choice distribution in Table 1.
9 We also checked whether the distribution of realized choices in the I- and NI-treatments differ. Based on a
Kolmogorov–Smirnov test, the null hypothesis of identical distributions cannot be rejected (p = 0.289).
10 The importance of using a human choice distribution is justified in light of the evidence of Bolton et al. (2005).
They implemented a random move procedure in which they varied the probability distributions and showed that the
distributions had an impact on perceived fairness.
294 A. Falk et al. / Games and Economic Behavior 62 (2008) 287–303
the show-up fee in case they occurred. We used the experimental software z-Tree (Fischbacher,
2007) to run the experiments.
4. Predictions
In the following we derive the theoretical predictions for our experimental game. First, we
present the economic prediction based on the assumption that it is common knowledge that all
players are selfish and rational, and then describe the predictions of different fairness theories.
4.1. Self-interest prediction
If it is common knowledge that all players are selfish and rational, the following subgame
perfect equilibrium outcome is predicted: B will always choose b = 0 in both treatments, i.e.,
she will neither punish nor reward, because any other choice is costly. Therefore, player A will
choose a = −6 in the I-treatment because he only loses if he chooses a > 0 and has nothing to
fear if a < 0. A random device determines player A’s move in the NI-treatment.
4.2. Fairness predictions
We now turn to the predictions of recently developed fairness theories and focus on player B’s
behavior. The models by Bolton and Ockenfels (2000) and Fehr and Schmidt (1999) are built on
the assumption that subjects dislike inequity. In the Bolton and Ockenfels model, inequity averse
players have a concern for a fair relative share of the total payoffs. The fair relative share is
defined as 1/n where n is the number of players in the game. If a player receives less than the fair
relative share, he tries to increase his share and vice versa. According to Fehr and Schmidt (1999),
inequity averse players are concerned with the payoff differences between themselves and each
other player. If player i’s earnings differ from those of player j, he aims at reducing the payoff
difference between himself and j. Both models predict that people exhibit reciprocal behavior for
sufficiently strong inequity aversion, i.e., b is increasing in a and b = 0 if a = 0. Both approaches
neglect intentions; only the payoff consequences are assumed to explain reciprocal responses.
This implies for our experiment that reciprocal responses between the I-treatment and the NItreatment
should be exactly the same for a given move of A. Since the payoff consequences
of A’s move are the same in both treatments, a player B who is solely concerned with payoff
consequences should respond in the same way.
A different concept of reciprocity starts with the premise that kind or unkind intentions exclusively
trigger reciprocal responses (Dufwenberg and Kirchsteiger, 2004).11 It immediately
follows from this premise that there should be no reciprocal behavior at all in the absence of fairness
intentions, i.e., player B neither rewards nor punishes but pursues her material self-interest.
Therefore, Dufwenberg and Kirchsteiger predict no reciprocal behavior at all in the NI-treatment
(b = 0, ∀a). The prediction for the I-treatment is less clear because the model exhibits multiple
equilibria, and some of them are compatible with b being locally decreasing in a. This is
11 The model of Dufwenberg and Kirchsteiger is based on Rabin’s (1993) normal form theory of fairness. Since the
present game is a sequential game, we restrict our analysis to the Dufwenberg and Kirchsteiger theory of sequential
reciprocity.
A. Falk et al. / Games and Economic Behavior 62 (2008) 287–303 295
Table 2
Summary of predictions for player B
Model I-treatment NI-treatment
Standard prediction b = 0, ∀a b = 0, ∀a
Only payoff consequences matter b increases in a exactly the same behavior
(Fehr/Schmidt and Bolton/Ockenfels) as in I-treatment
Only fairness intentions matter b increases in aa b = 0, ∀a
(Dufwenberg/Kirchsteiger)
Payoff consequences and fairness b increases in a b increases in a but less
intentions matter (Falk/Fischbacher) than in the I-treatment
a See discussion in the text.
so because according to the model, higher values of a do not necessarily signal more friendly
intentions.12 There are, however, plausible equilibria where a > 0 signals good intentions and
a < 0 signals bad intentions. In these equilibria, b is increasing in a (in the I-treatment).
Finally, the model by Falk and Fischbacher (2006) combines a concern for a fair distribution
of payoffs with the reward and punishment of fair and unfair intentions. The model makes the
(unique) prediction in the I-treatment that b is increasing in a. This reciprocal pattern is predicted
to be weaker in the NI-treatment than in the I-treatment. Contrary to Dufwenberg and
Kirchsteiger, the model does not predict b = 0, ∀a since players in this model not only have a
concern for intentions but also for a fair distribution of the payoffs. However, since intentions
are absent in the NI-treatment, subjects react less reciprocally than in the I-treatment. The latter
prediction distinguishes Falk and Fischbacher from the inequity aversion models by Bolton
and Ockenfels and Fehr and Schmidt. Table 2 summarizes all predictions. Notice that all fairness
theories make similar predictions in the I-treatment but differ in their predictions for the
NI-treatment.
5. Results
A total of 112 subjects participated in the experiment (66 in the I-treatment and 46 in the NItreatment).
All subjects were students from the University of Zurich or the Swiss Federal Institute
of Technology in Zurich, no economics students among them. The experiments were conducted
in June 1998. 1 point in the experiment represented 1 Swiss Franc (CHF 1 ≈ .65 US$). Subjects
received on average CHF 22.20 in the I-treatment and CHF 24.10 in the NI-treatment (including
a show-up fee of CHF 10). On average, the experiment lasted 45 minutes.
Our main result is shown in Fig. 1,13 where we plot the rewards and sanctions of B in both
treatments, i.e., we show the impact of B’s decisions on A’s payoff for each of his possible ac-
12 To make this point clear, consider the following example. Assume that B believes that A expects B to punish a = −5
with b = −6 while B is expected not to punish a = −6. In this case, the expected payoffs of B, πB, are higher if
a = −6 (πB = 6) than if a = −5 (πB = 1). This means that a = −6 does in fact signal more friendly intentions than
a = −5, which in turn justifies the higher punishments. Thus, it is possible in the Dufwenberg and Kirchsteiger model
that a = −5 is punished more than a = −6 in equilibrium. This discussion shows that an appropriate evaluation of the
Dufwenberg–Kirchsteiger model requires the elicitation of (higher order) beliefs. While we have not done this in this
study, other studies have used the measurement of higher order beliefs to test theories based on psychological game
theory (Dufwenberg and Gneezy, 2000; Charness and Dufwenberg, 2003).
13 We restrict our attention to the behavior of players B in this section. In Appendix A we also present player A’s
decisions for the I-treatment and the random moves in the NI-treatment.
296 A. Falk et al. / Games and Economic Behavior 62 (2008) 287–303
Fig. 1. Rewards and sanctions of players B dependent on decisions of players A.
tions. For instance, if A chooses a = 6 in the I-treatment, then he receives on average 6.55 points
from B (see rightmost unfilled circle). The corresponding median value is 9 points.
The figure reveals that Bs the behavior of A’s in the I-treatment. Average and median rewards
are increasing in the level of the transfer. Similarly, the more A takes away from B, the more B
is willing to sanction. This behavioral pattern is in clear contradiction to the standard economic
prediction (b = 0, ∀a). It is, however, well in line with the predictions of all fairness theories.
Figure 1 also reveals that behavior differs remarkably in the NI-treatment compared to the Itreatment.
On average, sanctions and rewards are much weaker in the NI- than in the I-treatment.
Average sanctions and rewards only differ from zero for sufficiently high or low values of a in
the NI-treatment. The treatment differences between the I- and the NI-treatments are even more
pronounced if we look at the median behavior. Median behavior does not show any reciprocal
pattern in the NI-treatment, but completely coincides with the prediction of the self-interest
model.
Are the differences between the I- and the NI-treatments statistically significant? Table 3
provides the answer. As in Fig. 1, it shows the impact of B’s decision on A’s payoff for all of
A’s moves. In addition to the average and median impacts, it also shows quartile values. These
distribution measures indicate that Bs’ reciprocal responses are not only weaker on average in the
NI-treatment, but that the whole distribution is shifted towards zero. For example, if A chooses
a = −6, both average sanctions are lower (1.43 instead of 8.09), as are the first quartile and the
median values. This holds (weakly) for all “take” decisions. Similarly if A chooses a = 6, for
example, not only are average rewards lower (1.39 instead of 6.55) in the NI-treatment, but all
A. Falk et al. / Games and Economic Behavior 62 (2008) 287–303 297
Table 3
Behavior of players B—Distribution measures and statistical significance
Player A’s move a −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
I-treatment
Average −8.09 −6.91 −5.97 −4.70 −2.97 −2.73 −.88 1.24 1.73 2.64 4.58 3.64 6.55
First quartile −18 −15 −12 −9 −6 −3 0 0 0 0 3 0 1
Median −9 −9 −6 −6 −3 −3 0 2 3 4 6 6 9
Third quartile 0 0 0 0 0 0 1 2 4 6 8 10 12
NI-treatment
Average −1.43 −2.35 −1.52 −2.26 −.30 −.57 −.78 .57 −.39 −.30 1.65 1.09 1.39
First quartile 0 −3 −3 −6 −3 −3 0 0 0 0 0 0 0
Median 0 0 0 0 0 0 0 0 0 0 0 0 0
Third quartile 0 0 0 0 0 0 0 1 2 5 5 7 8
Significance of difference
between treatmentsa
.001 .016 .023 .025 .031 .032 .109 .032 .006 .017 .002 .069 .001
a Significance is checked by means of the non-parametric Mann–Whitney U-test. Numbers are p-values. Given our
hypothesis that reciprocal responses are weaker in the NI-treatment than in the I-treatment, we used a one-sided test
(except for the (random) move of a = 0, where we have no such hypothesis.
distribution measures as well. Again, this holds (weakly) for all “give” decisions. We present
the results of the nonparametric Mann–Whitney U-test, which was run to check whether the
decisions of the Bs different across treatments, in the last row of Table 3. Behavior is indeed
significantly different across treatments at the five percent level for almost all a > 0 and a < 0; it
is significant at the ten percent level for a = 5.
Given the results shown in Table 3, we can reject the predictions by Bolton and Ockenfels
(2000) and Fehr and Schmidt (1999). Behavior in the NI-treatment is significantly different from
that in the I-treatment for all “give” and “take” decisions. Put differently, our results indicate that
intentions matter on an aggregate level both in the domain of positive as well as in the domain of
negative reciprocity.
The behavioral relevance of fairness intentions can also be shown with the help of regression
analysis. Table 4 shows the results of a regression model where the impact of B’s decision is
regressed on A’s move (a). We also include a dummy variable for the I-treatment (I) and an
interaction term a × I in this model. This specification allows us to estimate different linear fits
for the I- and the NI-treatments and thus to asses the difference between the two treatments. The
result of this regression is shown in Table 4. The coefficient of the interaction term a × I is highly
significant, while the dummy variable for the I-treatment (I) does not differ significantly from
zero. This means that while there is no difference between the treatments for a = 0, the reciprocal
responses of the Bs are stronger for sufficiently high or low a in the I-treatment compared with
the NI-treatment. This result confirms the statistical test presented in Table 3.
Furthermore, the regression allows us to test whether reciprocity is completely eradicated in
the NI-treatment, as predicted by Dufwenberg and Kirchsteiger (2004). Figure 1 shows that there
are weakly reciprocal choices for high enough “give” and “take” decisions on average, but does
this reciprocal behavior differ significantly from b = 0? The constant and the coefficient of a
shown in Table 4 measure the behavior of the Bs in the NI-treatment. Notice that the constant is
insignificant. If the random device determines a = 0, Bs neither reward nor sanction on average.
The coefficient of a is, however, positive and (weakly) significant. We thus conclude that, on
average, Bs reward positive and sufficiently high a values and sanction negative and sufficiently
low a values in the NI-treatment. To check the robustness of this finding, we also calculated the
298 A. Falk et al. / Games and Economic Behavior 62 (2008) 287–303
Table 4
Regression with impact of B’s decision as a dependent variable
Variable Coefficient
constant −.401 (.550)
A’s decision a .295* (.157)
dummy for I-treatment I −.522 (1.086)
a × I .907*** (.222)
Robust standard errors are in parentheses (subject ID as cluster variable).
There are 728 observations in 56 clusters. The F -statistic
equals 20.89; p < .001.
* Significance at the 10% level.
*** Significance at the 1% level.
Spearman rank correlation between the average impact of B’s decisions on A’s payoff and the
corresponding moves by A. The resulting coefficients are 0.8721 for the NI-treatment and 0.9945
for the I-treatment. Both coefficients are significant at any conventional level (p < 0.001). Thus,
significant reciprocal responses occur in the NI-treatment, even though reciprocal behavior is
considerably weaker in this case. Although rewards and punishments are quantitatively small,
the results suggest that reciprocal behavior is not solely intention-driven, but that fair outcomes
also play a role.
We have restricted our analysis to aggregate behavior up to now. However, since Bs had to
indicate a decision for each of A’s possible actions, we can also study individual patterns of
behavior.14 The first column in Table 5 shows the percentage of subjects who neither reward nor
sanction, i.e., whose behavior follows the standard economic prediction (b = 0, ∀a). The second
column reports the percentage of subjects who reward or sanction. The percentage of subjects
who exhibit positive as well as negative reciprocity is given in column 3. The percentage of
those who reward are listed in column 4 while the percentage of those who sanction are listed
in column 5. The sixth column, finally, consists of subjects whose rewarding or sanctioning
behavior is very unsystematic. Most of these subjects rewarded a particular transfer and—at the
same time—sanctioned a higher transfer.15
Table 5 shows that individual behavioral patterns between the two treatments are quite different.
First notice that the percentage of choices that coincides with the prediction of the
self-interest model (b = 0, ∀a) sharply increases in the NI-treatment (30 percent) relative to
the I-treatment (zero percent). This difference suggests that a non-negligible amount of reciprocal
behavior is exclusively a response to fairness intentions. Subjects who would reward or
sanction in the I-treatment refrain from doing so (and choose b = 0) because the actions of As
are determined randomly and do not signal any intentions.
This interpretation is also consistent with the second result in Table 5 (see column 2): the
percentage of subjects who are either positively or negatively reciprocal drops from 76 percent
in the I-treatment to 39 percent in the NI-treatment. This (highly significant) difference indicates
14 In Appendix A, where we show all individual decisions, we also indicate how each subject is assigned to the different
behavioral categories.
15 Two other subjects included in this category always indicated the exact same action (but not b = 0) for all possible
transfers of player A. Note that (except for rounding errors) the sum of numbers in columns 1, 2 and 6 adds up to
100 percent. Note that while the behavior classified as “other patterns” seems quite unsystematic, it is in principle
possible that these subjects act according to a reciprocity model in the spirit of Dufwenberg and Kirchsteiger holding
non-monotonous beliefs.
A. Falk et al. / Games and Economic Behavior 62 (2008) 287–303 299
Table 5
Individual patterns of behavior of Bs (percent)a
Selfish Reward or
sanction
Reward and
sanction
Reward Sanction Other
patterns
I-treatment (n = 33) 0 76 40 61 55 24
NI-treatment (n = 23) 30 39 18 35 22 30
Significance of difference
(Fisher’s exact test, p-values)
.001 .005 .052 .037 .011 .607
a The classification is constructed as follows: First, all subjects who show “other patterns” (column 6) are sorted out.
This category contains (i) subjects with a negative correlation between a and b, (ii) subjects who reward a decision a
while sanctioning a higher “give” decision a > a and (iii) subjects with an unconditional non-zero transfer decision. The
rest of the subjects is classified into the other categories. Subjects who never reward or sanction (b = 0), are assigned to
the first column. Subjects who reward an a > 0 at least once or sanction an a < 0 at least once are assigned to the second
column. Subjects who reward an a > 0 at least once and sanction an a < 0 at least once are assigned to the third column.
Subjects who reward an a > 0 at least once are counted in the fourth column and subjects who sanction an a < 0 at least
once are assigned to column 5.
that many reciprocal players are only willing to reward or sanction if the corresponding action
by A signals fair or unfair intentions. However, reciprocity in the NI-treatment is not completely
eradicated. Almost 40 percent of the subjects show some reciprocal behavior. We take this evidence
(which is in line with the regression results presented in Table 4) as a further indication
that reciprocal behavior is not solely intention-driven, but also by concerns for fair outcomes.
The fraction of subjects who exhibit both positively and negatively reciprocal behavior is also of
interest. Column 3 shows that 40 percent of the subjects in the I-condition and 18 percent in the
NI-condition exhibit this pattern. Thus, the possibility of inferring intentions also raises the percentage
of subjects who exhibit both types of reciprocity significantly. Columns 4 and 5 further
support our previous conclusion that fairness intentions significantly increase the willingness to
reciprocate and that there is a non-negligible percentage of people who reciprocate, even in the
absence of fairness intentions.
A final observation from Table 5 is worth noting. According to many fairness models, a person
should either not respond reciprocally at all or show both positively and negatively reciprocal
behavior. Fehr and Schmidt, for example, assume that the disutility arising from a disadvantageous
inequality is at least as strong as the disutility that arises from an advantageous inequality.
This implies that a player who rewards should also punish. Similarly, most reciprocity models
assume a single parameter for both positive and negative reciprocity. This implies that a player
who rewards also punishes and vice versa. In contrast to these predictions, Table 5 reveals that
21 percent of the subjects in the I-condition reward but do not punish. Likewise, 15 percent of
the subjects punish but do not reward.
6. Discussion
Although the behavioral relevance of intention is very intuitive, it has been quite difficult to
provide clean evidence for the behavioral relevance of fairness intentions up to now. We have
discussed several potential reasons for this and designed an experiment that avoids potential confounds
with other sources of reciprocal behavior. Our results provide evidence that people not
only take the distributive consequences of an action but also the intention it signals into account
300 A. Falk et al. / Games and Economic Behavior 62 (2008) 287–303
when judging the fairness of an action.16 This result casts serious doubt on the consequentialist
practice in standard economic theory that defines utility of an action solely in terms of its consequences;
it further shows that the models of fairness by Bolton and Ockenfels (2000) and Fehr
and Schmidt (1999) are incomplete to the extent that they neglect “nonconsequentialist” reasons
for reciprocally fair actions.
Different approaches have been proposed for incorporating intentions into fairness models.
Rabin (1993), Dufwenberg and Kirchsteiger (2004), Falk and Fischbacher (2006), and Cox et al.
(2004) consider the choice set of a player and infer the intention of a particular choice from the set
of possible alternatives. If, for example, there is no choice at all—as in our random treatment—
no intention can be inferred from a particular move. If, however, a player actually has the choice
between kind and unkind actions, the choice of a kind action allows inferring kind intentions
and vice versa. Falk et al. (2003) conducted four mini-ultimatum games to directly test whether
choice sets actually matter. In their experiment, one allocation x remains constant (8 points for
the proposer and 2 for the responder) in all four games, while the allocation y (the “alternative”
to x) differs from game to game. Although the outcome of the allocation x was constant, the
rejection rate of this allocation varied depending on the available alternatives. It was highest
(44%) when a fair alternative (5,5) was available and lowest (9%) when the alternative was even
more unfair (10 for the proposer, 0 for the responder). Brandts and Sola (2001) found a similar
result, also showing that the choice set determines the perception of fairness of an outcome, as
predicted by the models mentioned above.
The reciprocity models explain the difference between the I- and NI-treatment. However, we
also observe that there is reciprocity even in an environment where actions do not signal any
intention. Thus, the fairness of the outcome matters as well. This implies that the pure intention
models of Rabin (1993) and Dufwenberg and Kirchsteiger (2004) are also incomplete; unlike
reciprocity models that combine intentions with distributional concerns, such as Falk and Fischbacher
(2006).
Levine (1998), and Charness and Rabin (2002) choose another approach for incorporating
intentions. In these models, the players differ in an individual parameter—the player’s type. This
type measures the player’s kindness. The chosen alternative allows estimating this parameter.
More kind players choose more kind offers and therefore the estimate of this parameter can be
interpreted as the player’s intention. If player 1 chooses to take 6 points in our experiment, for
example, one can infer that he is a rather unkind type, while nothing can be concluded about
player 1’s type in case of a random first move. Since players base their reciprocation on the
assessment of the other player’s type, these models predict the main difference between the Iand
the NI-condition under reasonable assumptions. These models, however, fail to explain the
existence of players who do both, reward and punish in the NI condition.
16 An interesting application in the context of labor relations is whether incompetence is viewed and punished similarly
to unfair intentions. We think that the answer to this question depends on whether an agent has the capability of delivering
a good outcome but is just not trying hard, or whether he is actually incapable of providing a good outcome. In the former
case, there should be reciprocal punishment since incompetent results are likely to be caused by laziness (which is a
form of unkindness) and bad intentions. In the latter case, however, punishments should be less pronounced since a bad
outcome can neither be attributed to laziness nor bad intentions.
A. Falk et al. / Games and Economic Behavior 62 (2008) 287–303 301
Acknowledgments
This paper is part of the Research Priority Program on the “Foundations of Human Social
Behavior” at the University of Zurich. We thank Simon Gächter and Chiara Gulfi for valuable
comments.
Appendix A
Table A.1
Decisions of players A in the I-treatment
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
Number of A-players 4 2 2 3 1 0 3 2 5 2 0 1 8
Percentage of A-players 12 6 6 9 3 0 9 6 15 6 0 3 24
Table A.2
Random moves of players A in the NI-treatment
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
Actual number of random moves 2 0 0 0 1 1 2 2 5 1 2 1 6
Percentage of random moves 9 0 0 0 4 4 9 9 22 4 9 4 26
Table A.3
Individual data of players B in the I- and the NI-treatment (see Table 5 for explanations)
Treatment −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 Reward Sanction Never reward
nor punish
Other
patterns
I 4 2 0 9 7 8 2 4 4 5 7 6 10 x
I 0 0 0 0 0 0 0 1 2 3 4 5 6 x
I 0 0 0 0 0 0 0 1 2 4 6 7 9 x
I 0 0 0 0 0 0 0 2 4 6 8 10 12 x
I 0 1 2 3 4 5 6 7 8 9 10 11 12 x
I 0 0 0 0 0 0 0 2 3 7 8 10 12 x
I 0 0 1 1 2 2 2 3 6 6 12 12 18 x
I −3 −2 −2 −1 −1 −4 1 1 5 6 7 5 1 x x
I −6 −2 −3 −2 0 −1 0 0 0 1 4 7 10 x x
I −4 −4 −4 −4 −4 −4 −1 1 2 2 3 5 6 x x
I −5 −4 −3 −3 −2 −1 0 2 3 4 4 5 5 x x
I −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 x x
I −6 −5 −5 −2 −2 −1 0 2 3 5 7 8 8 x x
I −2 −2 −2 −1 −1 −1 0 2 4 5 8 9 12 x x
I −5 −4 −4 −4 −1 −1 0 2 4 6 8 9 11 x x
I −4 −4 −4 −3 −2 −1 0 2 4 6 8 10 12 x x
I −6 −5 −5 −5 −1 −1 0 2 3 6 8 10 10 x x
I −4 −4 −4 −3 −3 −2 3 4 5 7 9 11 13 x x
I −6 −6 −6 −5 −4 −3 0 2 4 6 8 10 12 x x
I −6 −5 −4 −3 −2 −1 0 2 4 6 8 10 12 x x
I −6 −5 −1 −1 −2 −2 0 0 0 0 0 0 0 x
I −1 −1 −1 −1 −1 −1 0 0 0 0 0 0 0 x
I −3 −3 −2 −2 −1 −1 0 0 0 0 0 0 0 x
I −5 −5 −4 −3 −2 −1 0 0 0 0 0 0 0 x
(continued on next page)
302 A. Falk et al. / Games and Economic Behavior 62 (2008) 287–303
Table A.3 (continued)
Treatment −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 Reward Sanction Never reward
nor punish
Other
patterns
I −6 −6 0 0 0 0 0 0 0 0 0 0 0 x
I −1 17 −4 18 −3 2 −6 18 18 18 18 −6 18 x
I 3 −4 4 −5 3 −6 1 0 −6 4 6 −2 18 x
I −5 5 1 −4 6 0 4 3 2 −3 2 14 1 x
I 3 −2 1 −1 0 5 2 0 3 −2 3 −4 3 x
I 0 3 1 0 0 2 −2 0 3 0 4 0 2 x
I −1 −6 −5 −4 −4 −3 −6 −6 −6 −6 −6 −6 −6 x
I −6 −6 −6 −6 −6 −6 −6 −6 −6 −6 −6 −6 −6 x
I 12 12 12 12 12 12 12 12 12 12 12 12 12 x
NI 0 0 0 0 0 0 0 0 1 5 6 7 8 x
NI 0 0 0 0 0 0 0 1 2 3 4 6 8 x
NI 0 0 0 0 0 0 0 2 5 6 6 7 8 x
NI 0 0 0 0 0 0 0 1 2 4 6 8 10 x
NI −2 −6 −4 −3 −3 −1 0 0 2 6 4 9 0 x x
NI 0 −1 −1 −2 −1 −1 0 5 3 6 7 12 15 x x
NI −1 −2 −3 −1 −2 −1 −1 1 2 5 7 9 11 x x
NI −2 −1 −1 −1 0 0 0 1 2 4 5 7 8 x x
NI −3 −3 −3 −2 −2 −1 −1 0 0 0 0 0 0 x
NI 0 0 0 0 0 0 0 0 0 0 0 0 0 x
NI 0 0 0 0 0 0 0 0 0 0 0 0 0 x
NI 0 0 0 0 0 0 0 0 0 0 0 0 0 x
NI 0 0 0 0 0 0 0 0 0 0 0 0 0 x
NI 0 0 0 0 0 0 0 0 0 0 0 0 0 x
NI 0 0 0 0 0 0 0 0 0 0 0 0 0 x
NI 0 0 0 0 0 0 0 0 0 0 0 0 0 x
NI −4 −6 8 −4 12 4 −2 10 −4 −6 2 −4 −6 x
NI 1 8 −1 −4 6 2 0 −2 5 3 1 −5 0 x
NI 0 3 4 1 6 3 0 1 2 −2 0 15 0 x
NI 0 −3 −1 −2 1 2 3 4 −4 −5 5 −6 0 x
NI 0 0 −2 3 −1 −1 0 2 4 5 0 5 0 x
NI 2 1 1 0 −2 −3 −3 −3 −4 −5 −5 −5 −6 x
NI 0 0 0 1 1 0 0 0 −1 0 0 0 0 x
References
Abbink, K., Irlenbusch, B., Renner, E., 2000. The moonlighting game—An experimental study on reciprocity and retribution.
J. Econ. Behav. Organ. 42, 265–277.
Andreoni, J., Miller, J., 2002. Giving according to GARP: An experimental test of the consistency of preferences for
altruism. Econometrica 70, 737–753.
Bewley, Truman, 1999. Why Wages don’t Fall during a Recession. Harvard Univ. Press, Harvard.
Blount, S., 1995. When social outcomes aren’t fair: The effect of causal attributions on preferences. Organ. Behav.
Human Dec. Proc. 63, 131–144.
Bolle, F., Kritikos, A., 2001. Distributional concerns: Equity- or efficiency-oriented? Econ. Lett. 73, 333–338.
Bolton, G., Ockenfels, A., 2000. ERC—A theory of equity, reciprocity and competition. Amer. Econ. Rev. 90, 166–193.
Bolton, G.E., Brandts, J., Ockenfels, A., 1998. Measuring motivations for the reciprocal responses observed in a simple
dilemma game. Exper. Econ. 1, 207–220.
Bolton, G.E., Brandts, J., Ockenfels, A., 2005. Fair procedures: Evidence from games involving lotteries. Econ. J. 115,
1054–1076.
Brandts, J., Charness, G., 2000. Hot and cold decisions and reciprocity in experiments with sequential games. Exper.
Econ. 2, 227–238.
A. Falk et al. / Games and Economic Behavior 62 (2008) 287–303 303
Brandts, J., Solà, C., 2001. Reference points and negative reciprocity in simple sequential games. Games Econ. Behav. 36,
138–157.
Camerer, C., Thaler, R., 1995. Ultimatums, dictators, and manners. J. Econ. Perspect. 9, 209–219.
Cason, T., Mui, V., 1998. Social influence in the sequential dictator game. J. Math. Psych. 42, 248–465.
Charness, G., 2004. Attribution and reciprocity in an experimental labor market. J. Lab. Econ. 22, 665–688.
Charness, G., Dufwenberg, M., 2003. Promises & partnership. Working papers in Economics 2003-3. Stockholm Uni-
versity.
Charness, G., Rabin, M., 2002. Understanding social preferences with simple tests. Quart. J. Econ. 117, 817–869.
Cox, J., 2004. How to identify trust and reciprocity. Games Econ. Behav. 46, 260–281.
Cox, J., Friedman, D., Gjerstad, S., 2004. A tractable model of reciprocity and fairness. Working paper. University of
Arizona.
Dufwenberg, M., Gneezy, U., 2000. Measuring beliefs in an experimental lost wallet game. Games Econ. Behav. 30,
163–182.
Dufwenberg, M., Kirchsteiger, G., 2004. A theory of sequential reciprocity. Games Econ. Behav. 47, 268–298.
Engelmann, D., Strobel, M., 2004. Inequality aversion, efficiency, and maximin preferences in simple distribution experiments.
Amer. Econ. Rev. 94 (4), 857–869.
Falk, A., Fischbacher, U., 2006. A theory of reciprocity. Games Econ. Behav. 54 (2), 293–315.
Falk, A., Fehr, E., Fischbacher, U., 2000. Testing theories of fairness—Intentions matter. Working paper No. 63. Institute
for Empirical Research in Economics, University of Zurich.
Falk, A., Fehr, E., Fischbacher, U., 2003. On the nature of fair behavior. Econ. Inquiry 41 (1), 20–26.
Fehr, E., Gächter, S., 2000. Fairness and retaliation—The economics of reciprocity. J. Econ. Perspect. 14, 159–181.
Fehr, E., Schmidt, K., 1999. A theory of fairness, competition, and cooperation. Quart. J. Econ. 114, 817–868.
Fischbacher, U., 2007. z-Tree: Zurich toolbox for readymade economic experiments. Exper. Econ. 10 (2), 171–178.
Gouldner, A., 1960. The norm of reciprocity. Amer. Sociological Rev. 25, 161–178.
Güth, W., Huck, S., Muller, W., 2001. The relevance of equal splits in ultimatum games. Games Econ. Behav. 37 (1),
161–169.
Huang, P.H., 2000. Reasons within passions: Emotions and intentions in property rights bargaining. Oregon Law Rev. 79,
435–478.
Kagel, J., Wolfe, K., 2001. Tests of fairness models based on equity considerations in a three-person ultimatum game.
Exper. Econ. 4, 203–220.
Kahneman, D., Knetsch, J.L., Thaler, R., 1986. Fairness as a constraint on profit seeking: Entitlements in the market.
Amer. Econ. Rev. 76, 728–741.
Levine, D., 1998. Modeling altruism and spitefulness in experiments. Rev. Econ. Dynam. 1, 593–622.
Offerman, T., 2002. Hurting hurts more than helping helps. Europ. Econ. Rev. 46, 1423–1437.
Rabin, M., 1993. Incorporating fairness into game theory and economics. Amer. Econ. Rev. 83, 1281–1302.