Electronic copy available at: http://ssrn.com/abstract=1068973

1

Intentions and Reciprocity*

Anna Macko1 Jaideep Roy

2

May, 2007

Abstract

The perception of fairness of an offer in ultimatum type games may not only depend upon the

distributional aspects of the offer itself but also on the intentions of the proposer that an offer may

signal. Recovering intentions is subtle and may depend heavily upon the environment and

consequently on the construction of the game. For example, one aspect of the environment could be

the set of available alternative offers as studied in Falk et al. (2003). In this paper we report an

experiment and provide evidence of a new aspect of an environment, which is related to the notion of

temptation in a mini ultimatum type game that affects perception of fairness. Two games are put to

test. In both games, a proposer has two available offers, fair and unfair, to choose from and the fair

offer is kept identical across the games. However, in one game the unfair offer is significantly more

skewed in favor of the proposer than the unfair offer in the other game. We show that the rejection rate

of the more unfair offer is systematically less than the rejection rate of the less unfair offer across the

two games.

Keywords: Ultimatum type games, fairness, temptation, intentions, reciprocity.

JEL Classifiers: D63, C78, C91.

* We thank Sandro Brusco, Debabrata Datta and Grazyna Wiejak-Roy for helpful comments. The usual

disclaimer applies. 1Corresponding author: Center for Economic Psychology and Decision Sciences, LKAEM, Ul. Jagiellonska 59,

03-301 Warsaw, Poland. Tel: +48 22 519 2204; Fax: +48 22 814 1156; Email: amacko@wspiz.edu.pl. 2 Department of Economics, School of Social Sciences, Brunel University, Uxbridge, Midlesex UB8 3PH,

United Kingdom. E-mail: Jaideep.roy@brunel.ac.uk

Electronic copy available at: http://ssrn.com/abstract=1068973

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Intentions and Reciprocity

1 Introduction

It is fairly well established by now that standard game theory predictions in many bargaining games

fail in experiments. One of the most widely studied games that confirm this is the celebrated

Ultimatum Game. In such games, two players are provided with an amount of money that they can

share. One of the players is randomly selected to play the role of a proposer who announces a share.

The other player, the responder, must then decide whether to accept or reject this proposed share. If he

accepts, then the announced share is implemented with certainty. On the other hand if the offer is

rejected, then both players receive nothing. Backward induction suggests that any offer with a positive

share going to the responder should be accepted (because something, no matter how small, is better

than nothing) while the responder is indifferent between acceptance and rejection if offered nothing.

Hence, it should be in the best interest of the proposer to offer a penny to the responder and claim the

rest for himself. No experiment carried out so far confirms this equilibrium play. For example, Guth et

al. (1982) observed that in an ultimatum game, the proposers on average demanded less than 70%

while about 20% of positive offers were rejected. This made the authors conclude that monetary

payoffs are not all that matters and there is the possibility of fairness considerations on part of the

players.3 Similar observations are confirmed by Camerer and Thaler (1995) and many others. For an

excellent survey on this, see Roth (1995).

Such systematic trends made economists infer that unfair proposals were rejected because the

responder derived higher satisfaction in punishing the proposer for being unfair than accepting an

unfair deal. A responder with such an attitude will be called fairness-driven henceforth. This attitude

has been shown to prevail in single period (or two-stage) models by Berg et al. (1995), Roth et al.

(1991), Cameron (1995) and Kahneman et al. (1986). A conjecture that follows logically from this is

that most proposers offered fair deals either because they were themselves fair or that they feared to be

3 Binmore et al. (1985) conducted an experiment on a 2-period bargaining game to observe that the distribution

of offers moved significantly towards the “standard” equilibrium and hence suggested that ultimatum games, or

games with a single bargaining period, are not good enough to draw conclusions regarding fairness attitudes of

players. In reply, Guth and Tietz (1988) tested two two-period games with significantly different discount

factors, to conclude that play was far from equilibrium predictions. This ambiguity was erased to a large extent

by the work of Ochs and Roth (1989) who, in an enlarged experimental design, confirmed that single-period

ultimatum games were not so much of a special case.

3

punished for making an unfair proposal. To see if proposals were fair because of the fear of

punishment or by true fairness considerations on part of the proposers, Forsythe et al. (1994)

compared offers between ultimatum and dictator games. They observed that proposals were more fair

in ultimatum than in dictator games. Bolton (1991) made similar reports on two-period bargaining

games where the last period is a dictator game. This brings up the issue that “although the strategic

environment is influenced by ideas about fairness, ideas about fairness are influenced by the strategic

environment”4 itself. This is central to our paper.

In general, it is implicitly assumed that a proposal is unfair if the distribution of payoffs recommended

by the proposal moves too much away in the direction that favors the proposer from the one with equal

shares. Let us call this distributional fairness. In a recent work by Falk et al. (2003), it is argued that a

responder’s perception of fairness of an offer may have more dimensions than merely its distributional

property. In this regard, they put to test a non-consequentialist approach to fairness where, apart from

the actual offer, what matters is the set of available offers. Thus, a proposal of (8,2), with 8 going to

the proposer and 2 going to the responder, is unfair if (a) the only other available offer was (5,5) but

not if (b) the only other available offer was (2,8). Their experiment, on what they call mini-ultimatum

games,5 shows that the (8,2) offer was rejected less frequently under scenario (b) than under (a). This

suggested that human perception of fairness does not rely simply on the distributional aspects of

offers, but may indeed be non-consequential where punishments associated with a failure to meet

fairness is dependent upon the judgments about the intentions that caused such violations. There is a

significantly large literature in psychology that deals with several notions and uses of intentions (see

Krebs (1970)). As Falk et al. argue, actions coupled with the environment (alternative available actions

in their case) in which such actions are taken work as signals for the possible intentions that lead to

such choices.

If indeed perceptions of intentions that an offer may generate in the given environment matter, as

demonstrated by Falk et al., the next step for us would be to check how robust such attitudes are

and/or to put to test such attitudes to more extreme situations. Hence, in this paper we propose a

similar (and more extreme) aspect of the environment, but different from that of “the set of available

alternative actions” as used in Falk et al., to suggest how similar actions in different environments may

signal different intentions and affect the perception of fairness. To ensure the exposition of our notion,

we modify the mini-ultimatum games as in Falk et al. in the following ways. There are two games that

4 Quotation from Roth (1995), page 271.

5 There are other works on such mini ultimatum games [see for example, Bolton and Zwich (1995) and Guth et

al. (2001)].

4

interest us in our experiment as depicted in figure 1. In Game 1 player 1 can either select to share 1000

(units of money) by offering 20 to player 2 (strategy X), or he can select to share only 100 in equal

proportions (strategy Y). In Game 2, player 1 has 100 to share, either by offering 20 to player 2

(strategy X) or sharing it equally (strategy Y). Player 2 decides whether to accept or reject a proposal.

Rejection (actions R or r) always yields zero to all players, while acceptance (actions A or a)

implements the chosen proposal of player 1.

Player 1 Player 1

X Y X Y

Player 2 Player 2

A R a r A R a r

980 0 50 0 80 0 50 0

20 0 50 0 20 0 50 0

Game 1 Game 2

Figure 1: The two games used in the experiment

In both these games, there are three Nash Equilibria in pure strategies (namely, (X, Aa), (X, Ar) and (Y,

Ra)). However, the only subgame-perfect equilibrium is the profile (X, Aa) in which player 1 plays X

while player 2 plays Aa, resulting in the unique outcome where player 2 receives 20, while player 1

receives 980 in Game 1 and 80 in Game 2. Moreover, the two games are payoff-identical for player 2.

Going by the standard notion of distributional fairness as discussed before, the proposal of (980,20) is

certainly more unfair than the proposal of (80,20). Given that the payoff distribution of the only other

option is held constant at (50,50) across the two games (and hence ruling out circumstances that affect

intentions a la Falk et al.), if at all responders are driven by fairness as defined before, one would

expect that the rate of acceptance of offer X in Game 1 cannot be more than that in Game 2. Perhaps

even more. Almost all experiments on Ultimatum games suggest that as the distributional unfairness

of an offer increases, so does the rate of rejection. Although the exact preferences of an average

responder and the likelihood of rejection needs more systematic study, in another recent experimental

study by Andreoni et al. (2003), a convex ultimatum game was under scrutiny in order to recover

preferences of the bargainers. In such a game, a given sum of money could be shared and the proposer

5

was asked to announce a share (in terms of fractions). The responder was then allowed to reduce the

given sum of money (on a continuous scale, hence the name convex). No reduction meant accepting

an offer in a standard ultimatum game while full reduction meant rejection. Allowing for intermediate

possibilities for a responder made his action set convex at each information set. Their experiment

provided very strong evidence that the likelihood of rejection (or the size of reduction of the original

sum of money) is indeed very sensitive to the announced fraction. Since the fraction of the pie that

goes to the responder is 20% in the offer (80,20) and only 2% in the offer (980,20) in our case, one

could expect the acceptance rate of the offer (980,20) to be far less than that of the offer (80,20).

The above conjecture may be successful in ultimatum games but may fail in our games since our

constructed environment has more subtle properties that affect perception of intentions of a given

offer. For example, from the perspective of the proposer, offering Y requires a far higher degree of

fairness-driven attitude in Game 1 than in Game 2. Putting it in other words, the offer X is far more

tempting in Game 1 than in Game 2 and hence even a reasonably fair proposer who would otherwise

propose offer Y in Game 2 may end up making the unfair offer X in Game 1. If a responder realizes

this and is fairness driven, by observing the offer X, what can he infer regarding the fairness-attitude of

the proposer in the two games? While, in Game 2, he would be almost sure that the proposer was an

unfair player, in Game 1 he may be less sure as to whether the proposer was indeed unfair or was “fair

but not fair enough” to resist temptation resulting from the strikingly high stakes in offer X in Game 1.

Consequently, while in Game 2 the responder will derive an extra pleasure from punishing a proposer

who makes the offer X, he will not be sure whether rejecting the offer X in Game 1 would lead to

punishing an unfair proposer or a reasonably fair one but weak, like many of us, under temptation.

Assuming that one does not like to punish those who are forced into environments where they may

easily give up principles of fairness, a fairness-driven responder may be less willing to enforce

punishment in Game 1 than in Game 2. Hence, and contrary to the standard notion of distributional

fairness, if fairness driven players indeed think in such terms, then one would expect the acceptance

rate of the unequal offer X not to be lower in Game 1 than in Game 2. We look for evidence of this

possibility in an experimental set up. In this respect, the dimension of the environment that we address

here is that of “the human capacity to be fair”. Arguably, it is an intangible aspect of our environment.

The modification of a standard mini-ultimatum game into our Game 1 is on purpose to enhance the

effect, if any, of temptation. We could have also used two other games by replacing our payoffs of

(980,20), (80,20) and (50,50) by, for example, (980,20), (800,200) and (500,500) respectively or by

(980,20), (650,350) and (500,500) respectively. Such payoff vectors would make both our games to be

6

mini-ultimatums. However, there are two major problems for our purposes: (1) the effect of temptation

would not be so prominent across the games and (2) the responder’s payoffs would not be identical

across games, leading to other unwanted and asymmetric reasons for acceptance of unfair offers.

Our experimental design is simple although we control for the following aspects that we consider

important. Firstly, a subject may feel that ultimatum-type games are by virtue unfair because proposers

tend to enjoy some first-mover advantages.6 This itself may lead to rejection of offer X. We wanted to

eliminate this aspect of “virtual unfairness” of ultimatum-type games by telling subjects before they

took part in our experiment that they will choose strategies both as a responder and as a proposer

(similar to that in Guth and Tietz (1988) and Andreoni et al.), and then we would randomly select the

role by which they will be paid. We also thought that the realization of the “mixedness” of the

intention-signal from offer X in Game 1 may be enhanced in those cases where the subject first makes

proposals. To our delight this indeed turned out to be true. Second, in this paper we do not wish to

address issues like how communication with and/or identity of the bargaining partner affect the choice

of strategies. Hence, we kept the design anonymous and non-communicable. Our research can be

easily extended to study the effects of these aspects. Thirdly, we use independent samples for each

game as we do not want experience in one game to affect the strategies taken in the other. Hence we

made sure that subjects playing both games came from a homogenous population. They were all arts

students from Warsaw and came from the same age group and social and educational background, and

there was no reason to doubt that they would differ distributionally in terms of bargaining games.

Our data has the following main implications for two-stage (one period) bargaining in ultimatum-type

games: (a) people can be easily tempted with very high stakes, in face of which they start making

distributionally unfair proposals with significantly higher frequency; (b) distributional unfairness in

face of strong temptation is generally reciprocated by a higher degree of tolerance than that in the

6 We made some preliminary enquiries amongst arbitrarily selected agents in the role of a responder to confirm

this fear. In many cases where the agent rejected offer X, when asked they said that they did so not only because

the offer in question was unfair but also because they found the game itself to be “unfair” as for the “same job of

making a decision”, a responder was given the possibility of earning significantly more. To get around this

“negative feeling” on part of the subjects, one could have first make the random selection for a role for each

subject publicly and then asked them to play the game in the randomly selected role. We tried this as well with

arbitrarily selected agents but those who were selected as responders told us that they felt unfair and defeated by

nature. Hence we thought that for our purposes, the random selection should be done after they make their

choices as this would minimize any such negative feelings in the role of responders. It also has an added

advantage of recovering bargainer-types as discussed in Section 3.3. In any event, we learnt that this is an

important and often overlooked aspect of ultimatum games.

7

absence of an any real temptation; and (c) people who have been put first in situations of strong

temptation are also most willing to pardon distributional unfairness resulting from temptation.

The rest of the paper is structured as follows. In section 2 we describe our experimental design on

games 1 and 2. In section 3 we report our findings. The paper concludes in section 4 with a discussion.

2 The Experimental Design

The experiment was performed on 160 subjects, who were undergraduate students from a private

business school and from a state university in Warsaw. We first divided them into four groups of size

40 each, called A, B, C and D. Groups A and B took part in Game 1 while groups C and D in Game 2

(these games are exactly as in Figure 1, excepting that the subjects were told that payoffs were in

points and that each 10 points carried 1 PLN = 0.3 USD approximately). Hence, Game 1 was carrying

a possible prize money of 98 PLN which is certainly a significant return for Polish students.

Subjects were made to sit in a classroom and we first described an example of a mini-ultimatum type

game. They were then told that they would take part in a similar game, both as a proposer as well as a

responder and in each case they will have to make their choices (more correctly, in order to ensure a

sufficiently large data set, we asked for their strategies as in Falk et al. and Andreoni et al.). They

were also told that some of them (but not all) would be randomly selected and paid according to their

choices, either as a responder or as a proposer, which will be decided by an independent toss of a coin

for each randomly selected subject. Moreover, they were told that their partners were from another

school in Poland and that their partners had already chosen their strategies (in exactly the same

environment as they were in our laboratory – while announcing this, we showed them paper files

which we said had their partner’s decisions).7 We also told our subjects that for each choice they make

(once as a proposer and once as a responder), they would be randomly paired with one of the subjects

of the other school. This essentially helped in minimizing any possible correlation between a particular

subject’s strategies as a responder and as a proposer in terms of the characteristic identity of the

7 In reality, we constructed the choices of the partners with the following rule: 1) all fair offers (Y) were

accepted, 2) 50% of the offers were X in both games and 3) 50% accepted unfair offers in both games.

Something similar but in a different context was used in Binmore et al. (1985). One may doubt the credibility of

such announcements in the minds of the subjects. However effects of this, if any, were far less important for our

purposes than those arising from any belief of a possible cooperation amongst bargaining partners.

8

bargaining partner. All payments were made immediately after all choices were made. We made sure

to announce that all random selections will be done publicly by one of them selected arbitrarily.

Groups A and C first made their choices as a proposer and then as a responder while groups B and D

did the same in the reverse order of roles. This was not made common knowledge amongst subjects.

Below we provide a table to summarize our subject groups in terms of games and orders of roles:

Group Game Order of roles

A Game 1 First propose, then respond

B Game 1 First respond, then propose

C Game 2 First propose, then respond

D Game 2 First respond, then propose

The exact instructions for groups A and B (which were in Polish) translated into English are provided

in Appendix A. Those for groups C and D are identical in language. In the next section we report our

results.

3 Results

3.1 Proposals

We first report the proposals across groups of subjects and across Games, as depicted in figures 2a and

2b, where on the y – axis we plot the observed percentage of the unfair proposal X.

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Figure 2a: Proposal X across groups of subjects Figure 2b: Proposal X across games

As the above figures show, 51.25% of proposals were unfair in Game 1 while only 28.75% of

proposals were unfair in Game 2. This difference is statistically significant (χ2 = 8.44, p < 0.004).

However, these proportions are comparable across groups A and B (52.5% and 50% respectively)

while they were visibly higher in D than in C (37.5% and 20% respectively) (χ2 = 2.99, p < 0.084).

This enables us to conclude that our subjects confirm that the offer X in Game 1 was significantly

more tempting. It is interesting to observe that the order of roles (that is whether subjects were first put

into a responders’ or a proposers’ task) has no effect in Game 1 (enforcing the fact that the temptation

to offer option X in Game 1 was independent of this order). On the other hand in Game 2, the group

that responded first, tend to have made the unfair offer X visibly more frequently.

3.2 Responses

We now turn our attention to the responder strategies. As expected, all subjects, barring 4 exceptions

out of 160, decided to accept the offer Y (with payoff (50,50)). The following figure reports the

responders’ choices against the unfair offer X.

52,50%50,00%

20,00%

37,50%

0%

25%

50%

75%

100%

A B C D

51,25%

28,75%

0%

25%

50%

75%

100%

A+B C+D

10

Figure 3a. Acceptance of unfair offers across Figure 3b. Acceptance of unfair

groups of subjects. offers across games.

In figures 3a and 3b, we depict on the y - axis the percentages of acceptance of the distributionally

unfair offer X across groups and games respectively. In general, this acceptance rate is visibly higher

in Game 1 (73.75%) than in Game 2 (62.5%). This difference, although not statistically significant, is

worth reporting (χ2 = 2.33, p < 0.123) and is sufficient to accept the following hypothesis:

Hypothesis 1

The acceptance rate of the offer X is observed at least as frequently in Game 1 as in Game 2.

Acceptance of the above hypothesis is a clear indication that there is more than mere distributional

aspects of fairness of a given offer. Keeping in line with the possibility of mixed signal of offer X and

the effect of experience of roles as discussed before, we formulated our main hypothesis as follows:

Hypothesis 2

1. Acceptance of the offer X is observed more frequently in group A than in group C.

2. Difference in the acceptance rates between groups A and C is bigger than the same between

groups B and D.

80,00%

67,50%

60,00%

65,00%

0%

25%

50%

75%

100%

A B C D

73,75%

62,50%

0%

25%

50%

75%

100%

A+B C+D

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For groups B and D who were first asked to respond and then to propose, this difference is not at all

significant with 67.5% and 65% being the respective percentages of acceptance across these two

groups. But most interestingly, for groups in the reverse order of roles, the level of acceptance in

group A (80%) is significantly higher (χ2 = 3.81, p < 0.051) than that in group C (60%). These

differences are not significant across groups A and B or across groups C and D. Finally, the difference

in the acceptance rate across groups A and C is bigger than the same across groups B and D (F = 64.5 ,

F(α = 0.1) = 39.86). Thus Hypothesis 2 is accepted by our experimental data.

3.3 Types of Bargainers

To be complete, we present the distribution of types of bargainers in our experimental dataset. A

bargainer-type is defined as the profile of strategies a subject takes once as a proposer and once as a

responder. Thus in a given game, there are 8 possible player types. However, we rule out types where

a player rejects the equal payoff offer of (50,50). Hence the types that interest us in this experiment are

)},(,{)},,(,{)},,(,{ aAYaRXaAX and )},(,{ aRY in either game. The distributions of these types

across the four groups and the two games are depicted in figures 4a and 4b respectively.

45,0% 45,0%

27,5%

15,0%

10,0%

0,0%

5,0%2,5%

42,5%

37,5%

22,5%

27,5%

40,0%

25,0%27,5%

17,5%

0,00%

10,00%

20,00%

30,00%

40,00%

50,00%

A B C D

X (A,a) X (R,a) Y (A,a) Y (R,a)

Figure 4a. Distribution of bargainer-types across groups

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45,0%

21,3%

3,8%5,0%

25,0%

40,0%

22,5%

32,5%

0,00%

10,00%

20,00%

30,00%

40,00%

50,00%

A+B C+D

X (A,a) X (R,a) Y (A,a) Y (R,a)

Figure 4b. Distribution of bargainer-types across games

Even casual observation reveals that the fraction of players, independent of the game or the sequence

of roles, who made an unfair offer almost never rejected unfair proposals. Hence the type {X,(R,a)} is

almost absent (similar to what was found in Andreoni et al.). The most popular type in Game 1 was

the one which made the unequal offer (980,20) and accepted all offers (type {X,(A,a)}, 45%) while

that in Game 2 is the one which offered the equal share (50,50) and accepted all offers (type {Y,(A,a)},

40%). However, the popularity of type {X,(A,a)} in Game 1 is significantly higher in both groups A

and B but that of type {Y,(A,a)} is closely followed by the type {Y,(R,a)} in both groups C and D for

Game 2 (32.5%). Moreover, the type {X,(A,a)} is higher in Game 1 than in Game 2 (χ2

= 10.19, p <

0.001) and in group A than in group C (χ2 = 8.57, p < 0.003). Similarly, the type {Y,(A,a)} is higher in

Game 2 than in Game 1 (χ2 = 4.10, p < 0.043). Finally, the type {Y,(R,a)} is higher in group C than in

group A (χ2

= 4.94, p < 0.026). The summarized data is put in a table in Appendix B. We now

summarize our main finding below:

Main Empirical Conclusion

There is evidence supporting the following possibilities:

1. Offer X is more frequently made in Game 1 than in Game 2.

2. Acceptance rate of offer X is systematically higher in Game 1 than in Game 2.

3. In groups where players first propose and then respond, the acceptance of offer X is

significantly more frequent in Game 1 than in Game 2.

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4 Discussion

Our experiment provides evidence that there are more aspects in the perception of fairness of a payoff

vector than simply its distribution or the set available alternatives as we have shown that the

distributionally more unfair offer of (980,20) is accepted more frequently than the offer (80,20) when

the available set of alternative offers is held constant at only (50,50). We argued that this may occur

due to the players’ understanding that while the offer (80,20) was most likely to have come from an

unfair proposer, since 980 is far too tempting to be resisted on face of a mere 50, when an offer of

(980,20) is made, a responder may discount his belief regarding the unfairness of the proposer by the

amount of temptation in the environment. In this sense, the responder looks at an offer as a screening

device to tell apart the possible types of a proposer. In Game 2, the offer (50,50) gives a signal that the

proposer is fair with a high probability while the offer (80,20) gives a signal that he is unfair with a

high probability. On the other hand in Game 1, while the offer (50,50) remains to be a signal that the

proposer is fair with a high probability (and possibly higher than that in Game 2), the offer (980,20) is

less informative and hence may indeed be a pooling signal. We may interpret our group data

percentages as these belief probabilities.

Let us once again take a careful look at the games used in Falk et al, in particular the 2-8 game and the

5-5 game. In the former, the only two options for the proposer are (8,2) and (2,8) while in the latter

game these are (8,2) and (5,5). In their experiment Falk et al. observe that the percentage of

acceptance of the (8,2) offer in the 2-8 game is significantly higher than that in the 5-5 game. The

most plausible reason for this could be that responders would hardly expect even a reasonably fair

proposer to offer a distribution that is unfair to himself. Hence, the (8,2) offer in the 2-8 game gives a

mixed signal regarding intentions of the proposer while the same offer in the 5-5 game pushes the

responder to believe with very high probability that the proposer was not a fair person. Something

similar is also the case in our experiment. However, the difference is that in our case, intentions are

not dependent upon the available alternative proposals but rather on the perceived weakness of human

nature that a proposal along with the environment in which it is made highlights. In this sense, our

observation is perhaps a more consequential one, by which we demonstrate that the argument a la Falk

et al. may not necessarily have to be non-consequential.8 On the other hand our experiment supports

8 We are aware that the border between consequentialism and non-consequentialism is not easily well drawn and

there are some grey areas.

14

the issue of intentions a la Falk et al. and shows that this aspect is not only robust but can also be

applied to even more extreme environments.

On a different note, consider classical preferences without fairness and temptation. Suppose that there

is a fraction of the population who simply use dominated strategies (that is rejection of an unfair offer

in an ultimatum-type game). According to our data, about 30% of our 160 subjects reject unfair offers.

Given this, one may ask the following question: what is the optimal strategy of a rational proposer in

this case? Since one does not know whether the opponent is rational, it may be rational to offer the fair

division. Furthermore, it is likely that offering the fair division may be optimal in the 'small stakes'

game (Game 2) but not in the 'high stakes' game (Game 1). In the first case an unfair offers yields an

expected sum of (7/10)(80) = 56 which, with a little bit of risk aversion on part of the proposer, may

yield a utility less than the utility of 50. In the high stake game this expected utility is obviously

significantly higher and hence even a highly risk averse proposer may find it optimal to make the

unfair offer in Game 1. However, one can still make the point that fairness and temptation matter,

since the percentage of rejection is lower in a high stake game. Thus, our predictions are valid even if

only a minority of the players are affected by these factors.

4.1 Related Literature from Psychology

Several other psychological aspects in decision making may have their independent effects on the

strategies taken by our subjects. In this section we provide a brief outline of these aspects which call

for further experiments, perhaps by psychologists. In doing so, we divide such psychological traits into

two groups, namely, interactive factors and non-interactive factors.

Interactive factors

Interactive factors are those possible psychological traits of a decision maker in retrospect with an

environment where he requires an understanding of the psychology of other simultaneously active

decision makers. Hence, these factors are more central to game theoretic environments.

Let us look at the Game 1 from the perspective of a proposer. On one hand he would like to earn a lot

of money but on the other hand he would like to be fair – either because he is a fairness-driven person

or because he is afraid that an unfair offer will be rejected and he will get nothing. For a person who

first plays in the role of a responder, the understanding of how difficult is the situation of a proposer

15

depends on his own ability and willingness to empathize with a proposer. This willingness to

empathize may have been initiated in our experiment by the fact that our responders knew that they

will be later asked to play in the role of a proposer. As a result, responders who were able to empathize

were arguably also able to imagine the perspective of a proposer. And taking other’s perspective into

consideration, as suggested by experiments carried out by psychologists (for example, see Manner et

al. (2002)) is one of the factors that increase the likelihood of pro-social (benefiting others) behavior.

Taking the perspective of one’s bargaining partner (in our case a tempted proposer) should be easier

and more pronounced in case of those responders who experienced earlier a role of a proposer. Thus it

could be expected that such subjects would be even more likely to “forgive” proposers making unfair

offers than those who took the perspective of a proposer without experiencing his role. Hence in spite

of a much higher distributive unfairness of proposal X in Game 1, the willingness to punish unfairness

should not be (and actually was not) stronger in Game 1 than in Game 2. And within Game 1 those

who experienced proposing first (group A) were even less likely to punish the unfair offer X. Our data

supports this.

Non- interactive factors

Non-interactive factors are those traits in the minds of a decision maker which may be applied in

isolation to perceptions regarding the attitudes of the other decision makers active simultaneously. In

this sense, these factors are of less importance to a game theorist although psychologists are typically

more interested in this area. In what follows we list some of these non-interactive factors which may

be relevant in our experimental environment.

Proposing the option X violates the norm of fairness. Transgressing, or knowingly committing a

wrongful act (e.g. violating a widely recognized norm), leads to an arousal of a negative internal state

– or guilt. It is well supported in the psychology literature that the feeling of guilt is accompanied by

attempts to reduce this highly aversive state usually by some altruistic deeds (see for example Krebs

(1970), Regan (1971) and Baumeister and Stillwell (1991)). Hence being a proposer in Game 1 and

succumbing to temptation (choosing the option X) should evoke in some people the feeling of guilt.

Playing next the role of the responder provides them with a good opportunity to reduce guilt by a

“beneficent deed” – accepting an offer X. Such a pattern of behavior is actually observed when we

compare groups A (Game 1) and C (Game 2). Another non-interactive factor that could also contribute

to the results is good mood. Again, it is also well documented in the psychology literature that positive

affective states lead to more pro-social, altruistic behavior (Isen, 2000). Recently Kirchsteiger et al.

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(forthcoming) have studied the impact of moods in gift-exchange games to show that people are more

generous when acting under good moods. In our case, Game 1 gives to a proposer a possibility of

earning a lot of money, which may lead to the arousal of good mood. Being in a good mood when

playing the role of a responder may lead to altruistic behavior – accepting unfair offers. Thus more

acceptance of offer X should be observed in Game 1 than in Game 2 and this is evident from our data.

Since a subject playing the role of a proposer first (group A) has this possibility of earning money

highlighted best, the intensity of good mood should be strongest in those subjects than in those who

play the role of a responder first (group B) or those who play Game 2. If the results are driven by

intensity of good mood, the acceptance of the unfair offer should be higher in group A than in all other

groups. This is actually what was observed, although the difference between groups did not reach

statistically significant levels.

These two factors of course do not exhaust the list of possible factors underlying the reasons why

subjects accepted unfair offers. Other factors such as convincing oneself that one does not suffer from

jealousy (by accepting unfair offer) in order to reassure a subject’s high self-esteem is also worth

considering.

Each of the above described factors may be tested in more controlled environments. The feeling of

guilt could be tested in a very simple experiment. If the results are driven solely by guilt then giving a

guilty proposer (who has just proposed offer X) a chance to reduce this before he plays the role of

responder should lead to lower acceptance of unfair offer by those subjects. We reserve such

experiments for future research.

Fairness and intentions are multidimensional and hence difficult aspects of a strategic environment

and no one experiment can reveal the entire spectrum of these subtle notions. We consider our

experiment as a small step towards unraveling this seemingly difficult area of research.

Appendix A: Instructions

The following is the written instruction (translated into English from Polish) given to each subject who

played Game 1 (that is for groups A and B). Instructions for Game 2 follow the same manner of

communication and hence is not provided here.

17

Instructions for a Proposer

You are asked to share some points with another person. To do this, you have two options X and Y

from which you will have to select just one.

Option X: 1000 points will be shared between the two of you in the following proportions:

You will receive 980 points and the other person will receive the remaining 20 points.

Option Y: 100 points will be shared between the two of you in the following proportions:

Both of you will receive 50 points each.

Your Options

Option X Option Y

You get 980 You get 50

Other person gets 20 Other person gets 50

But

Before payments are made to you and the other person, the other person will be asked whether

he/she accepts the option you have chosen or rejects your choice.

• If the other person accepts your choice then payments will be made according to the option

you have chosen.

• If the other person rejects your choice, then both (that is you and the other person) will

receive nothing

Your Options

Option X Option Y

Other person’s choice Other person’s choice

for option X for option Y

Accept Reject Accept Reject

You get 980 You get 0 You get 50 You get 0

Other person gets 20 Other person gets 0 Other person gets 50 Other person gets 0

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Which option would you choose?

Write down your choice of option (that is X or Y) in the box provided below.

End of instructions.

Instructions for a Responder

You are asked to share some points with another person. To do this, you have two options X

and Y from which you will have to select just one.

Option X: 1000 points will be shared between the two of you in the following proportions:

You will receive 20 points and the other person will receive the remaining 980 points.

Option Y: 100 points will be shared between the two of you in the following proportions:

Both of you will receive 50 points each.

Other Person’s Options

Option X Option Y

You get 20 You get 50

Other person gets 980 Other person gets 50

But

Before payments are made to you and the other person, the you will be asked whether you accept the

option the other person has chosen or reject the other person’s choice.

• If you accept the other person’s choice then payments will be made according to the option the

other person has chosen.

• If you reject the other person’s choice, then both (that is you and the other person) will receive

nothing.

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Other Person’s Options

Option X Option Y

Your choice for option X Your choice for option Y

Accept Reject Accept Reject

You get 20 You get 0 You get 50 You get 0

Other person gets 980 Other person gets 0 Other person gets 50 Other person gets 0

Suppose the other person chooses Option X. Will you accept (A) or reject (R) this option?

Write down your choice (that is A or R) in the box provided below.

Suppose the other person chooses Option Y. Will you accept (A) or reject (R) this option?

Write down your choice (that is A or R) in the box provided below.

End of instructions.

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Appendix B: Data

Subject Group A B A + B C D C + D

Number of subjects making offer X 21 20 41 8 15 23

Number of subjects accepting offer X 32 27 59 24 26 50

Bargainer-Type X,(A,a) 18 18 36 6 11 17

Bargainer-Type X,(R,a) 1 2 3 0 4 4

Bargainer-Type Y,(A,a) 11 9 20 17 15 32

Bargainer-Type Y,(R,a) 7 11 18 16 10 26

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