Are there peer effects in reciprocity? : evidence from a trust experiment

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“Are there peer effects in reciprocity?” Evidence from a trust experiment

Master thesis University of Amsterdam Faculty of Economics and Business

Rafael van der Steen (10668888) Supervised by Joël van der Weele

Abstract. This research investigates peer effects in reciprocal decision-making using a modified trust

game. Existing theory suggests that people’s behavior depends on conformism and preferences of fairness and if they have a certain reference point, they act according to it. Based on these mechanisms, I give my first (high) treatment group a reference point consisting of people acting reciprocally and my second (low) group a reference point with people that act rather self-interestedly. With the trust game (Berg et. al., 1995) I test whether this treatment affects reciprocal decisions, i.e. whether the high treatment group shows higher reciprocity levels than the low group. I find indications of peer effects in these reciprocal decisions, although I am not able to confirm all findings statistically because of a limited amount of observations. The discussion provides a hypothesis on how many observations would be needed for an identical research to give significant statistic results and gives recommendations for further research.

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1. Introduction

Imagine you are transferred to another department at work that has a completely different work environment. Your new colleagues are generous to each other and everyone helps each other with their work, while at your former department the people only thought about their own interests and were reluctant to return a favor when it would cost them any effort. Do you adapt yourself to this new environment? You probably do. Why this happens and if this also happens in anonymous situations is researched in this paper.

This paper examines peer effects in reciprocity. Reciprocity is a frequently recurring principle in everyday life and is for example reflected in several policy decisions. Two simple examples are the labor and the investment market (Gächter & Fehr, 2002; Kahan, 2003). Labor contracts are generally based on reciprocity. The employer pays the employee and in return the employee does effort. But will more money result in more effort? It might be useful for an employer to take into account the kind of business he is dealing with. A raise in salary may have considerable positive effects on effort in one firm, but much less in another. The work environment of the employees and how they influence each other could cause this difference. Another example of how knowledge about peer effects in reciprocity can be relevant is for investors. Investor relations are strongly based on reciprocity. An investor logically expects something in return from the party he invests in, so he should be careful about the kind of party he is investing in. If it is the case that people adapt their reciprocity to what others do, an investor probably wants to consider how reciprocal for example investment bankers or stockbrokers in general are. These examples indicate why it is important to know about peer effects in reciprocity.

In addition to the existing literature about reciprocity and the mechanisms behind peer effects, I perform an experiment using an adaptation of Berg’s et. al. (1995) trust game. This game, also known as the investment game, provides a simple way to measure both trust and trustworthiness. In the game, subjects are randomly divided into pairs, where one is player A and the other player B. Both players initially have an equal endowment. In the first stage, which is about trust, player A may send some of his endowment to B. The amount player A sends will be exogenously tripled. In the second stage, which is about trustworthiness, Player B has to decide how much to return to A. I will use player B’s decision in this game as a measurement of the reciprocity of the players. That is also the main reason for using this particular game; it provides a good indication of reciprocity and besides it can be easily adapted in a way that it is possible to measure peer effects in reciprocal decisions. The part of the experiment that enables me to measure peer effects and makes my research different from others is that I give my two treatment groups different benchmarks, consisting of decisions made by other players in a previous, very similar, version of this game.

This feature is the main difference between a paper by Mittone and Ploner (2011), where this research is partly derived from. They investigated the effect of peer pressure on the trustworthiness of people, also using the trust game. Although the approach to peer effects and the experimental design are different, the underlying (psychological) mechanisms are similar in our researches.

These mechanisms behind reciprocity and peer effects will be discussed in Section 2. That section also provides an overview of empirical evidence from historical trust game experiments. Section 3

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describes the experimental design and concludes with the hypothesis. In Section 4 the results of the hypothesis tests are presented, together with elaborate findings of the experiment. Section 5 gives a general conclusion and provides a discussion for further research.

2. Existing literature

a. The concept of reciprocity

The concept of reciprocity is a much-debated topic. There are several definitions, of which one is given by Sobel (2005, p. 392): “Reciprocity refers to a tendency to respond to perceived kindness with kindness and perceived meanness with meanness and to expect this behavior from others.”

When considering reciprocity, a distinction can be made between instrumental and intrinsic reciprocity (Sobel, 2005). The former represents actions of self-interested agents that are aimed at sustaining a long-term relationship in order to build reputation or to obtain the highest long-term profit. Intrinsic reciprocity represents individual preferences that are willing to exchange own consumption for consumption of others in response to kind behavior and are willing to sacrifice own consumption to decrease the consumption of others in response to unkind behavior. Regularly both types of reciprocity result in identical decisions, only the underlying preferences leading to this decision are different. When an individual makes a reciprocal decision that is intrinsically motivated, it can be seen as a single decision that increases her or his utility. When the exact same decision is instrumentally motivated, it should be seen as part of a strategy with goals reaching further than this single round. Johnsen & Kvaløy (2014) tried to distinguish these types in an experimental study. Their main findings were that subjects anticipate instrumental reciprocity, i.e. they are aware that people make reciprocal decisions based on self-interested preferences and take that into account when making their decision. On the other side, people reward reciprocal decisions that are based on purely intrinsic motivations. An intrinsically motivated decision is rewarded more than an instrumentally motivated one, although in real life situations this distinction is often hard to recognize and thus to anticipate on. The reason why it is important to make this distinction is that is helps to understand why certain reciprocal decisions are made. More specifically, it may explain why people make difference choices in one-shot situations compared to repeated situations.

The following story gives an example of instrumental reciprocity. During the 1980s scientist Robert Axelrod set up a tournament in which professors in social science could submit strategies to participate in a 200 times iterated version of the Prisoner’s Dilemma game. This game consists of two players that both have the option to cooperate or defect. Both players cooperating leads to a higher equal payoff than both defecting, but if the other cooperates, you’re best off by defecting, which gives you the highest possible payoff. This game is much analyzed in order to test cooperation in human behavior. The strategy that won the Axelrod’s tournament was submitted by Anatol Rapoport and is called ‘Tit for Tat’. This strategy starts with cooperating in the first round and subsequently imitates whatever the opponent did in the previous round. This well-known strategy in game theory is all about reciprocity. It rewards good (cooperative) behavior and punishes bad (defective) behavior.

Rapoport came up with this strategy to obtain the highest long-term profit. When long-term profits and/or reputation are involved in reciprocal decisions, these can explain this reciprocal behavior.

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Although even without the presence of one of these two, people tend to reciprocate by rewarding nice behavior and punishing bad behavior (Mui et. al., 2002). In my experiment I am looking at this intrinsic reciprocity, since there is no possibility for strategies. This type of reciprocity is reflected in personal and business interactions of which a (similar) recurrence is absent or they are not assumed to be repeated. This behavior is sometimes hard to explain by standard economic theory based on the selfishness and rationality of humans. Behavioral economists try to provide answers to this phenomenon (Camerer et. al., 2011). Researchers such as Fischbacher, Fehr & Gächter (2000; 2001) and Tversky & Kahneman (2000; 2003a; 2003b) did extensive research on this topic and provided explanations based on e.g. altruism or inequality aversion. People concerning for the welfare of others and the preference for fairness are possible reasons for repaying trust in a trust game, even in an anonymous setting (Camerer, 2003). Cox (2002) studied the reasons behind the trustworthiness more closely and compared the amount returned in a trust game with the amount allocated in a dictator game. The reason he made this comparison is to distinguish the reasons for repaying trust. He measured altruism with the dictator game and researched if reciprocity could explain the difference in outcomes between the dictator and the trust game. A dictator game is equal to the second stage in the trust game, i.e. the decision of the B player, only without any history. The dictator may split an amount between him and a responder, but the responder has no option but to accept. Because the dictator game has only one stage and is completely anonymous, giving away something as a dictator would mean pure altruism. The second stage in the trust game adds a possibility for reciprocity. Cox found that the repayments in a trust game were only slightly higher than the amount a dictator would allocate. This means that the repayment is mostly based on altruism and is increased a little bit because of reciprocity.

b. Historical trust game experiments

In the original trust game (Berg et. al., 1995) players A trusted on average $5.16 out of their $10 endowment to player B. The average amount B returned to A was $4.66. Other historical trust games showed similar outcomes: Cox (2004) found a player A’s mean transfer of $5.97 and a player B’s mean return of $4.94 and Ben-Ner & Putterman (2009) found a player A’s mean transfer of $5.47 and player B’s mean return of $7.42. In both experiments the subjects had an endowment of $10. On the other hand, researchers that compared different nationalities playing this game found very diverse results. Koford (1998) found that Bulgarian students were very trusting and trustworthy, which turned out by investing 70 percent of their endowment and getting 150 percent in return. Willinger et. al. (2003) compared Germans and French people and found that the French trusted much less than the Germans in the first stage, but they returned similar amounts in the second stage. These results indicate that trust can differ considerably between cultures. Other researches found differences between gender (Chaudhuri & Gangadharan, 2003; Buchan et. al., 2008), age (Sutter & Kocher, 2007) and other population characteristics. Besides, this game has been used to test how the possibility of punishment affects trust (Charness et. al., 2008) and the relation between contracts and trust (Ben-Ner & Putterman, 2009).

Analyzing these results, it is interesting to see that on average the A players trust about half of their endowment to player B. When considering this game from a game theoretical approach, player A should not trust anything to B. Because this is an anonymous one-shot game, reputation does not play a role. This makes the B player a dictator with no incentive to return anything to A. Anticipating

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on this, a rational A player should not send anything. Although this outcome is far from efficient, it is the subgame-perfect Nash equilibrium.

c. Peer effects in several fields

People act differently in groups compared to private decision-making. A majority of the people adjusts their decisions in real life situations to what others do. Hargreaves Heap’s (2014) explanation for this is that people’s behavior depends on conformity. When they have information about the behavior of others, their preferences make them decide in the same direction. Related to this Abeler et. al. (2011) did research about reference points and found that when people have different reference points, they behave differently. More specifically, they behave in the direction of this point. According to this, exogenous preferences of individuals are no longer given. This conformist behavior is tested and confirmed in several public good games with a possibility for punishment (e.g. Brandt et. al., 2003). The option of punishment in this case is used to punish people that contributed below average, independent of the average. This means that they do not actually care about how much others contribute, but more about whether they contribute similar to other people. Carpenter & Matthews (2005) researched whether this behavior stemmed from conformism or preferences of fairness and found evidence of both. The main difference between these concepts, is that fairness is about an equal division of goods, where conformism drives people to make similar decisions, independent of whether they are fair or not. This conformist behavior and people’s preferences for fairness, combined with the fact that people’s decisions depend on their reference point, can explain why there are peer effects in reciprocity, if I find this result in this research.

The following studies demonstrate examples of fields in which peer effects have already been found. Multiple authors discovered effects in e.g. drinking, drug use and anti-social behavior (Gaviria & Raphael, 2001; Bayer et. al., 2009). When comparing peer effects in different situations, a distinction can be made between peer effects in social outcomes, such as drinking, and effects on productivity, such as academic outcomes. Sacerdote (2011) found that the measured peer effects on the former one are larger than on the latter. Zimmerman (2003) considered the effects on productivity and researched peer effects in academic grading. He found that students with roommates that have higher grades are more likely to get higher grades themselves, because they take over their study behavior. The students with the higher grades drop a bit in their productivity, but this effect is less strong. Also Falk and Ichino (2006) examined peer effects in productivity. They found that people that are being watched by someone have a higher productivity than people working on their own. Again, the one with the lower productivity adapts to the more productive one, more than vice versa. As mentioned before, Mittone and Ploner (2011) investigated the effect of peer pressure on the trustworthiness levels of players in a trust game. They came up with the evidence that agents whose choices were observed tend to reciprocate more than agents that made anonymous choices. This is an example about peer effects in reciprocal decisions.

When we relate the conformist behavior of people discussed in the previous subsection to the concept of reciprocity, it is interesting to consider how these two relate. Hargreaves Heap (2014) give two main reasons how this behavior can be explained. The first one is that people see the behavior of others as a signal about the state of the world. This form of signaling influences their behavior. In real life, asset price bubbles could be explained according to this reasoning. He also discusses information cascades, a phenomenon that takes place when people attach too much value

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to the evidence of behavior of others compared to their own value, which may lead to inefficient outcomes. In everyday life this happens when people buy rising stocks, rationalizing the rise by the private information of others, despite of their own consideration. The second one is the dependency of people’s preferences on social comparison. The comparison in this context is about behavior. People receive utility when they compare their behavior with others and notice that they are not outliers. According to this theory, the availability of information about the behavior of others makes people behave in the same manner.

Based upon this theoretical background, I will present the experimental design, followed by the hypothesis.

3. Experimental design

a. Trust game

I conducted two sessions at the Center for Research in Experimental Economics and Political Decision making (CREED) lab of the University of Amsterdam, one for each of the treatments. In both sessions 24 subjects participated. The subjects were recruited from the CREED’s database of interested students. Both sessions were run in a large laboratory with 36 cubicles and were all provided with a computer. No one was allowed to participate in more than one session. This experiment was part of a multiple experiment project with six other experiments that were part of another student’s master thesis. The subjects received a €7 show-up fee and one of the seven experiments was randomly chosen for payment. On average, each subject earned €19 in a two-hour session. The instruction sheets that were used during the experiment can be found in Appendix B.

In the experiment, the subjects play a slightly adjusted version of the trust game, originally set up by Berg et. al. (1995). The game works as follows. The subjects are randomly divided into pairs, where one is player A and the other player B. Both players are initially endowed with 10 points. In the remainder of the experiment the subjects are told that these points will be converted to actual euros. Player A may send some (between 0 and 10 integer points) of his points to B. The points player A sends to B will be tripled by me, so B will receive 3 times the number of points player A sends. For example, if A sends 2 points to B, B will receive 6 points. If A sends 9 points to B, B will receive 27 points. Player B has to make 10 decisions. For every possible amount A can send (0 up to 10), she or he has to choose the amount she or he would return to A, except for 0. The B players can maximally return what they receive, i.e. if A sends 0, they automatically return 0. The reason why player B has to make 10 decisions instead of one, which is the case in the original trust game, will be explained in the remainder of this chapter. Player A will finally get the points she or he has kept plus the points B returns to her or him. Player B will finally get her or his own endowment plus the (tripled) amount of points received by player A minus the amount returned to player A.

Formally: A= 10 - SA + SB B=10 + SA*3 - SB

With A = Points A ends up with, B = Points B ends up with, SA = amount sent by A, SB = amount returned by B

The subjects are informed that when this experiment is chosen for payment, the points will be converted to actual euros at the rate of 1 point to €0,75 and that this game will be played only once.

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The experiment consists of two treatments. The subjects in the first session of the experiment will be in the first treatment group (high) and the subjects in the second session in the second treatment group (low). The subjects do not know that there was another treatment group. All the A players play the standard trust game and did not know about the treatment of the B players. The only decision they have to make is how many points to send to player B. The part that I added to this experiment to be able to involve peer effects, is that before the B players have to make their decisions, they are shown a distribution. This distribution shows reciprocity levels of players in an earlier, very similar, trust game, performed by Charness et. al. (2008). The reason for using a distribution is that it provides diverse information. It provides information about the decisions of all players of the earlier game by showing the subjects the proportion of players that chose different reciprocity levels. It provides the information that is needed to test how the reciprocity levels of others affect their own decisions. An average reciprocity level for example would not be suitable in this case, because it does not say whether all subjects decided around this average, or half of the people returned almost nothing and the other half almost everything. Why this game by Charness et. al. is chosen, together with the similarities and differences with my experiment, will be explained in the remainder of this section.

The x-axis of the distribution shows the proportion of points returned to player A in increments of 20%. This proportion is calculated as follows: if A sends 6 points to B, B receives 18 points. B returns 6 points. The proportion player B returns is 6 / 18 = 33%. The y-axis shows the percentage of players corresponding to that proportion. The high and the low group see different distributions, as shown below.

Figures 1A & 1B. Distribution reciprocity levels

A. Distribution shown to the high group B. Distribution shown to the low group

The high group sees a distribution in which the largest proportion of the players had a trustworthiness (proportion of points returned to player A) of 60-80%. In the distribution that is shown to the low group, the largest 20% share is 0-20%. For the convenience, we state that the first distribution represents reciprocal players and the second self-interested players.

The data that is used to make the distributions comes from the paper An investment game with third-party intervention by Charness et. al. (2008). They performed a very similar trust game

experiment at theUniversity College of Santa Barbara (UCSB), where they recruited students via a

university-wide email database of interested students. Their experimental design is similar; an 0 10 20 30 40 50 Per ce n tage o f p lay e rs Proportion returned to A 0 5 10 15 20 25 30 35 40 Per ce n tage o f p lay e rs Proportion returned to A

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anonymous trust game where players are able to send any integer amount between 0-10. Besides, similar instruction sheets were used in both our experiments (except for leaving out their treatment information). They performed three rounds in their experiment. I used the data of the first round for the distribution shown to the high group and data of the third round for the distribution shown to the low group. Since the reciprocity levels varied much between these rounds, I was able to make these two different distributions.

In addition to that I show my treatment groups these distributions, a difference with their design is that in my experiment the B players have to make decisions for every possible amount player A is able to send, instead of only for the amount A actually sends. This is called a strategy method (Selten, 1967). The reason for using this method is that it provides more information about a subject than a single decision, since it is possible to observe at what level the B players start to reciprocate more or less. This information would be absent if the B players saw the amount sent by A and subsequently made their decision, as in the paper by Charness et. al. (2008). Because I use this strategy method I am able to calculate the reciprocity levels for all possible trust levels of the A players, which gives a more complete picture of how reciprocal the players are.

While the B players can see the distribution, they have to make their decisions about how many points to return to player A, for every possible amount A is able to send, except for 0. After everyone made their decisions, the subjects are asked a few general questions about their age, nationality, gender, study and if they ever participated in a game theory course. The latter two in particular are important, since in most of the game theory courses and some Economics courses this game and the corresponding Nash equilibrium is discussed. It is reasonable to assume that subjects that followed such a course send less as an A player and also reciprocate less as a B player, since the subgame perfect Nash equilibrium indicates that the A player should not send anything to B, and B subsequently has nothing to return. After the subjects answered these questions the experiment is over.

b. Hypothesis

Reciprocal behavior can vary substantially between different situations. The same people can make different decisions in different environments and peer effects can be a cause of this (Perugini et. al., 2003). This given forms the base for creating my hypothesis. According to the subgame perfect Nash equilibrium, based on purely selfish preferences and full rationality, there would be no reciprocity at all. Since experimental evidence demonstrates differently, this equilibrium is not realistic.

Based on the altruistic behavior and fairness preferences (inequality aversion) of people, as discussed in Section 2, I assume that there is reciprocity. Since people’s reference point influences their decisions, because their behavior depends on conformity, I expect that there are peer effects in reciprocity. With the experiment I will test this hypothesis by providing my two treatment groups with two different reference points and see whether this influences their decisions. I expect that the high treatment group, which has a higher reference point, is more reciprocal than the low treatment group. Based on the mechanisms described here, I expect that when people have a reference point for the trustworthiness of others, they behave according to this. This comes from the fact that people receive utility from deciding in the same direction as others did (Hargreaves Heap, 2014). Besides, people act according to their reference point and are likely to change their decision when

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they have a different reference point (Abeler et. al., 2011). According to this, the high group should have higher reciprocity levels. If this is the case, the reciprocity level in the high treatment group should be significantly higher than in the low treatment group.

As mentioned in Section 2, the psychological mechanism behind this is that people tend to take over other people’s decisions and do not want to deviate from the average too much, because of their preferences for conformity (Hargreaves Heap, 2014). This is due to the fact that people like to have their behavior confirmed by others, which is a form of social comparison (Fischbacher et. al., 2001). When their behavior is confirmed, they are able to justify their decisions. Whether they want to justify against themselves, other players, or in this case the experimenter, is an interesting question that cannot be tested with this experimental design. Further research could try to differentiate between these groups and test which one is the strongest.

An interesting question behind the reason for this adaptive behavior is whether people learn something from the decision of others and therefore change their own decision, or that solely the fact that they do not want to be an outlier is sufficient to make them decide in the same direction. Unfortunately, I am not able to distinguish these explanations with my design.

4. Results

With the results of the modified trust game I can test my hypothesis. I will check if the decisions made by the B players and the corresponding trustworthiness in both treatment groups are significantly different. More specifically, I will control if the high group shows higher trustworthiness than the low group. With this outcome I can give a general explanation about how peer effects influence reciprocal decisions and thereby provide an answer to my research question.

The analysis will focus on the decisions of the B players. Because their decision is based on reciprocity and the decision of an A player on trust, the emphasis will be on B’s results. First, I will provide a summary of the subject information, before showing all the decisions made during the experiment. The data of the euros earned and age are averages. For nationality and study it applies that there were no other main nationalities and studies represented by the subjects, but a mixture of several nationalities and studies. The game theory variable indicates how many subjects have ever followed a game theory course during their study. Note: all digits in the results are rounded to a maximum of two decimals.

Table 1. Summary of subject information

Euros earned Age Nationality Gender Study Game theory

Session 1 (24 subjects) 18.54 23.79 23/24 (96%) Dutch 17/24 (71%) Male 14/24 (58%) Economics 13/24 (54%) Game theory Session 2 (24 subjects) 19.38 26.08 20/24 (83%) Dutch 14/24 (58%) Male 9/24 (38%) Economics 11/24 (46%) Game theory Total (48 subjects) 18.96 24.94 43/48 (90%) Dutch 31/48 (65%) Male 23/48 (48%) Economics 24/48 (50%) Game theory

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a. A players

Table 2 presents the decisions made by the A players during both sessions. Since the analysis focuses on the decisions of the B players, I will briefly discuss the A players. The decision of the A players is about trust. The A players must trust (part of) their points to the B player and subsequently hope or expect to get more points in return.

Table 2. Decisions player A

Subject # Session 1: A sends Session 2: A sends

1 4 0 3 0 0 5 4 0 7 9 0 9 0 0 11 0 4 13 0 0 15 0 4 17 5 10 19 9 5 21 2 0 23 3 0 Average 3 1.92 S.E. (0.97) (0.92)

The table shows that the average amount of points sent by A differs quite (not significantly at a 10% level, Mann-Whitney U test) between both sessions. This means that a comparison between the sessions should take this into account. Since there is no difference in the treatment of the A players, this average should not differ because of that. Because the number of observations is rather small (12 players), the explanation of the difference in both treatments stems most likely from differences in the preferences of the subjects. The higher fraction of Economics students and subjects that followed a game theory course in the first session could explain lower trust amounts, if they acted according to the Nash equilibrium (see Table 1). Since the opposite is true for the two sessions, I am not able to give an explanation for the difference between both sessions based on the available information.

The average amount sent by the A players in both sessions is considerably lower than in many previous experiments, which generally had results between 5 and 6. Since the game was similar in these experiments, the difference stems presumably from the subjects. Considering my subjects, a large proportion studied Economics and/or followed a game theory course. This could be an explanation of the small amount the A players have sent to B, because these subjects may think more rationally and self-interestedly because of their study contents and may be aware of the existing Nash equilibrium, which is to send nothing.

b. B players, Session 1

The B players in the first session (high treatment group) saw the distribution (Figure 1A) with the high reciprocity levels.

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Table 3 presents an overview of the decisions of these B players. Remember the B players had to make 10 decisions. For every amount A could send, they had to make a decision about how many points to return. If A sends 0, B has no option but to return 0, so this decision is left out of the table. The bottom of the table presents the average trustworthiness (TW). Trustworthiness levels are calculated as follows:

Trustworthiness level = SB / (SA*3) * 100

With SA = points sent by Player A, SB = points returned by Player B

Table 3. Session 1, Decisions player B Subject # Received: 1 2 3 4 5 6 7 8 9 10 6 2 4 6 9 12 14 16 18 20 23 18 0 0 0 0 0 0 0 0 0 0 14 0 0 2 4 5 6 7 8 9 10 16 0 0 0 0 0 0 0 0 0 0 22 1 1 1 2 2 2 3 3 3 3 24 1 3 4 6 7 9 10 11 12 14 10 0 0 0 0 0 0 0 0 0 0 8 0 1 3 4 5 6 8 8 10 9 12 1 3 4 6 7 9 10 12 13 15 2 2 3 4 6 6 8 9 10 12 13 4 1 2 3 4 5 6 8 10 13 16 20 1 3 4 6 7 9 10 12 13 14 Average 0.75 1.67 2.58 3.92 4.67 5.75 6.75 7.67 8.75 9.75 S.E. (0.22) (0.43) (0.57) (0.84) (1.05) (1.29) (1.45) (1.66) (1.88) (2.17) TW 25 27.78 28.7 32.64 31.11 31.94 32.14 31.94 32.41 32.5 S.E. (7.25) (7.20) (6.33) (7.00) (6.98) (7.14) (6.89) (6.93) (6.96) (7.22)

When considering the average, we see that the average amount returned by B is always lower than the amount sent by A, even though it will be tripled. 3 out of the 12 subjects did not return any points to A. It can be taken into account is that these 3 are all Economics students, of which 2 followed a game theory course. As mentioned before, these subjects could be well aware of the existing Nash equilibrium and acted according to it.

When we look at the average trustworthiness, we see that it increases with the amount sent by A, excluding a few exceptions. We can see this as a type of reciprocity. The more A trusts B, the more B relatively returns to A and the less A trusts B, the less B returns. This corresponds to the definition of Sobel given at the beginning of this paper; react to kindness with kindness and meanness with meanness. Nevertheless, the average trustworthiness is always less than 50%, which means that the B players on average return less than half of the (tripled) points they receive.

c. B players, Session 2

The second session (low treatment group) saw the distribution (Figure 1B) with the low trustworthiness levels. Table 4 presents all the decisions made by the B players in the second session.

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Table 4. Session 2, Decisions player B Subject # Receives: 1 2 3 4 5 6 7 8 9 10 20 1 2 3 4 5 6 7 8 9 10 10 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 1 2 3 4 8 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 24 1 2 3 4 5 6 7 8 9 10 6 1 2 3 4 5 6 6 7 7 8 14 0 1 2 4 7 8 10 12 13 15 4 1 2 4 4 5 6 6 7 7 7 22 0 0 0 0 0 1 2 2 2 2 18 1 3 4 6 7 9 10 12 13 15 16 0 0 2 2 3 3 3 5 5 6 Average 0.42 1 1.75 2.33 3.08 3.75 4.33 5.25 5.67 6.42 S.E. (0.15) (0.33) (0.48) (0.64) (0.84) (1.00) (1.10) (1.28) (1.38) (1.57) TW 13.89 16.67 19.44 19.44 20.56 20.83 20.63 21.88 20.99 21.39 S.E. (4.95) (5.43) (5.32) (5.36) (5.59) (5.52) (5.22) (5.33) (5.10) (5.23)

The averages in the second session are lower than in the first for all amounts. Again, the B players return, on average, less than they received. Equal to the first session, 3 out of 12 subjects did not return anything for every amount A could send to them. This time, none of them studied Economics and only one followed a game theory course. This means we cannot simply state from these results that if someone studies Economics or followed a game theory course this will mean that he is more likely to return nothing to the A player.

We observe a similarity in both sessions in the pattern of the trustworthiness levels. These levels increase with the amount of points A trusts to B. With a few exceptions, the level increases from 13,89% if A sends 1 point, to 21,39% if A sends 10 points. This increase is mostly present between the lower trust levels, which also applies for the first session. This finding shows that reciprocity increases faster when trust is increased from a low level, than from a high level to an even higher level (also see Figure 3 on the next page).

d. Comparison between the two sessions

Independent of player A´s decision, the average amount returned by B and the corresponding trustworthiness level are lower in the second session than in the first session. This applies for all amounts A is able to send. In the first session, the average amount returned by B ranged from 0.75 to 9.75 and in the second session from 0.42 to 6.42. These averages are significantly higher in the high treatment group at a 10% level (Mann-Whitney U-test), although not at a 5% level (p value=0.08). The single decisions made by the B players are not significantly different between both sessions for all levels of trust. The comparisons are shown in Figure 2.

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Figure 2. Average amount returned by B

The trustworthiness levels vary in the first session from 25% if A sends 1 point to 32,5% is A sends 10 points. For the second session these averages are respectively 13,89% and 21,39%. For all amounts, the trustworthiness is higher in the first session. The distributions are shown in Figure 3.

Figure 3. Trustworthiness levels of B

The average trustworthiness levels in both sessions are significantly different, using the Mann-Whitney U-test at a 5% significance level. Again, the single trustworthiness levels are not significantly different. This probably stems from the limited amount of observations. In the discussion I will give a hypothesis about how many subjects are required in a similar experiment to obtain significant results.

e. Group division of reciprocal types

The following analysis divides subjects in groups according to their reciprocal behavior. By grouping the subjects, it is easy to see whether a few subjects show a major change in their reciprocal behavior or that the majority of the subjects become a bit more selfish/reciprocal. I compare the group divisions for both sessions to make a statement about this.

0 2 4 6 8 10 12 1 2 3 4 5 6 7 8 9 10 A ve rag e am o u n t re tu rn e d b y B Amount sent by A Session 1 (high) Session 2 (low) 0 5 10 15 20 25 30 35 1 2 3 4 5 6 7 8 9 10 Tr u stwor th in ess level of B Amount sent by A Session 1 (high) Session 2 (low)

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This analysis is based on a group division by Fischbacher et. al. (2001). They performed an experiment with a public good game and based on the subjects’ choices they divided them into groups. The first group consisted of conditional cooperators, which were willing to contribute the more to a public good the more others contributed. They stated these people motivated their decisions based on altruism, inequity aversion and reciprocity. Another group consisted of free riders, which acted purely selfish and did not contribute anything, independent of what others contributed. Between these two extremes, they saw a group of people that had a ‘hump-shaped’ distribution of contributions, i.e. they were conditional cooperators up to a certain point, after which they started to reduce their contributions. The remainder did not have a clear pattern.

I will also divide the subjects of the trust game in these groups, except for leaving out the hump-shaped group since there were no subjects in my experiment with such a distribution. I call the free-riders group selfish, which fits better for a trust game. I will use the same requirements as Fischbacher et. al. (2001) did for the conditional cooperators group, which means that the Spearman rank correlation coefficient must be positive and significant (1% level) between the amount they receive and the amount they send. This gives the following results:

Table 5. Group division

Session 1 Session 2 Total

Conditional cooperators 8 6 14

Selfish 3 3 6

Other 1 3 4

Total 12 12 24

For subject specification see Appendix A

Both sessions contained three purely selfish subjects that did not return anything for every amount A sent. The difference between the sessions is that the first session had two additional conditional cooperators and two fewer subjects in the ‘other’ group. The subjects in the other group are much closer to the selfish group than to the conditional cooperators, since they all return very few points (see Figure 4 and 5). Besides, the conditional cooperators in the second session were less cooperative, meaning they were further away from the equal 50/50 diagonal, which implies that you act perfectly conditional cooperative. According to this group division we can see that the second session is less cooperative, although the fraction of conditional cooperators is not significantly different in both sessions (Fisher exact test, 5% significance level). Figure 4 and 5 show the difference in the average amounts returned by the different groups. The x-axis shows the amount A sent to B and the y-axis presents the average amount the B player in that particular group returned.

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Figure 4. Session 1, group division

Figure 5. Session 2, group division

This group division indicates that the shift between groups is rather small, two subjects move from conditional cooperator to the other group, but the shift within groups is quite large; the conditional cooperators in the Session 2 are less cooperative than the ones in Session 1. This suggests that the difference between the two sessions comes from a general shift in the behavior of the subjects, rather than a radical change in the behavior of a few subjects.

f. Regression analysis

I performed a regression with the following variables; return, treatment, gender, GT and study. Return is the amount of points the B player returned to A. All 10 decisions made by the B players are taken as single observations. Because these decisions are not completely independent, I will control for this by using robust standard errors. Treatment is a dummy variable, with value 1 for the high treatment group and value 0 for the low group. Gender is a dummy variable, with 1 for male and 0 for female. GT stands for the game theory dummy variable, with value 1 if that subject has ever followed a game theory course, and 0 if not. Study is a dummy variable with value 1 if the subject studies Economics, and 0 if she or he studies something else. Regressing the independent variables on the dependent return variable gives the following:

0 2 4 6 8 10 12 14 16 1 2 3 4 5 6 7 8 9 10 Cond. Coop. Selfish Other Diagonal 0 2 4 6 8 10 12 14 16 1 2 3 4 5 6 7 8 9 10 Cond. Coop. Selfish Other Diagonal

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All the variables have the expected positive or negative coefficient, although only the treatment variable is significant at a 5% level. Apart from the fact that I am only able to confirm it statistically for the treatment variable, the coefficients indicate the following. Being in the high treatment is positively related to your return as a B player, compared to the low treatment group. This is in accordance with the hypothesis that the high treatment group shows higher reciprocity levels. Being a male is apparently positively related to return. Nevertheless, I did not focus on gender effects in my research. Studying Economics and having followed a game theory course are negatively related to the amount returned as a B player. This is in line with the expectations I described before, explaining that these subjects could be aware of the Nash equilibrium, which is to return zero.

5. Conclusion and discussion

By using the existing literature on reciprocity and peer effects, supported by an adjusted trust game experiment, this paper tries to research how these concepts are related. The hypothesis is in line with the existing theories on reciprocity and peer effects. Various studies found that reciprocity can differ within subjects, depending on their environment. People’s reference point plays an important role in their decision-making. Combined with the fact that human behavior depends on conformity and people have preferences for fairness, I hypothesized that peer effects are present in reciprocity.

Because of these preferences, I assumed the players would adapt to other people’s decisions. I believe this adaptive behavior is even stronger when players are not anonymous, as they were in this game. Although my experiment is not able to test this difference, it could be an interesting research for the future.

I find that the high treatment group, which was shown a distribution of players with high reciprocity levels, showed higher reciprocity than the low treatment group. The average amount returned by the B players, as well as the corresponding trustworthiness level, was higher for all the amounts A trusted to B. Unfortunately, these averages were not significantly different.

Because this experiment was performed with a limited amount of subjects, a recommendation for further research is to perform this experiment with more subjects. My hypothesis is that an amount

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of subjects around 150 will be sufficient to give statistically significant results (at a 5% level). This hypothesis is based on the fact that when I tripled my subjects decisions (I had 48 subjects), i.e. as if every single decision was exactly repeated by two extra subjects, all the Mann-Whitney U tests gave significant outcomes, which means that in this case the differences are significantly different between the high and the low treatment group.

The regression did give a significant result for the treatment variable. This indicates that being in the high treatment group has a significant positive impact on the return as a B player. This provides a confirmation of the hypothesis that the high treatment group shows higher reciprocity levels than the low treatment group, indicating that peer effects are present.

The group division of different reciprocal types shows that the amount of selfish subjects remained the same, but the high treatment group contained two additional conditional cooperators instead of two in the other group, which is close to the selfish group. Together with the fact that the conditional cooperators in the low treatment group were further away from the equal 50/50 diagonal and thus less reciprocal, these findings indicate that the high treatment group is more reciprocal. Besides, this group division explains that the change in behavior between the two groups is due to a general shift in behavior of the subjects, rather than a radical change in the behavior of a few subjects.

Although some of the results of my experiment could not be statistically confirmed, all findings indicate that the subjects in the high treatment group show more reciprocity than in the low treatment group. This means that their reference point affected the decisions of the subjects.

The findings in this paper could add to the debates over reciprocity. They provide evidence about the importance of the environment reciprocity is measured in, since that determines the outcome to a large extent. This research demonstrates the presence of peer effects in reciprocal interactions, which may help to better understand how one’s individual decisions depend on the group behavior in real life trustworthiness relations. One may consider using this information for labor contracts policies or in the investment world. These fields deal with reciprocity on a regular basis and it is therefore useful for policy makers to take the findings and underlying mechanisms discussed in this paper into consideration.

Further research could focus on specific aspects in this research that remain unanswered. For example, trying to differentiate between the groups against whom subjects want to justify their behavior when they act according to what others do. Another interesting question could be whether peer effects become stronger when the relation is not anonymous. Concluding, there is still much to explore on the topic of peer effects in reciprocal behavior.

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7. Appendix

A. Group division per session and subject

Session 1 Conditional cooperators: #2,4,6,8,12,14,20,24 Selfish: #10,16,18 Other: #22 Session 2 Conditional cooperators: #4,6,14,18,20,24 Selfish: #8,10,12 Other: #2,16,22 B. Instruction sheets General instructions

Welcome to the experiment!

This is an experiment to study how people solve decision problems. This sheet contains the instructions explaining the way the experiment works. Please do not converse with the other

participants during the experiment. If you need any help, please, raise your hand and wait in silence. Someone will attend to you as soon as is possible.

The experiment is described as follows. In this experiment each of you will be divided randomly in pairs. You will not know who will be your partner either during or after the experiment. There will be 2 types of players in this experiment: A and B. For the moment, you don’t know which role will you play. Each A and each B player has been assigned an endowment of points. Each A will have the opportunity to send to the paired B some, all or none of his or her endowment. Each point sent to Player B will be tripled. For example, if A sends 2 points to B, B will receive 6 points. If Player A sends 9 points to B, B will receive 27 points. The points sent by A are subtracted from A’s total. Player B will decide how many points to send back to A, keeping the remainder.

The points you end up with will be converted to actual euros at the end of the experiment, if this experiment is chosen for payoff. This experiment is structured so that no one, including the experimenters, will know the personal decisions of people playing as A or B.

Please wait for a sign of one of the instructors, before continuing.

Game instructions (Player A)

You have been randomly assigned to the role of player A.

You are endowed with 10 points. You may send some (0 up to 10 integer points) of your points to B. The points you send will be tripled by the experimenter, so B will receive 3 times the number of points you send. For example, if you send 2 points to B, B will receive 6 points. If you send 9 points to B, B will receive 27 points. Your points (and B’s points) will be converted to actual euros at the rate of 1 point to €0,75, if this experiment is chosen for payoff.

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Player B is also endowed with 10 points. B will decide how many points to send to you (not tripled) for every possible amount you are able to send (0-10 integer points).

Finally, you will get the points you have kept plus the points B returns to you. Player B will get his endowment, plus the (tripled) amount of points he receives from you, minus the points he returns to you. There will be only one round of this game.

You have 10 points, how many points do you wish to send to Player B?

Game instructions (Player B – high treatment group)

You have been randomly assigned to the role of player B.

A has been endowed with 10 points and he or she must decide how many points to send to you. The points A sends are tripled by the experimenter, so you will receive 3 times the number of points A sends to you. For example, if A sends 2 points to you, you will receive 6 points. If A sends 9 points to you, you will receive 27 points. Your points (and A’s points) will be converted to actual euros at the rate of 1 point to €0,75, if this experiment of chosen for payoff.

You are also endowed with 10 points. You will decide how many points to return to A for every possible amount player A is able to send. This means you have to make 10 single decisions. When both you and player A have made their decisions, the amount of points A sends will be matched to your choice for that particular amount to determine the payoffs.

Finally, you will get your own endowment plus the (tripled) amount of points received by player A, minus the amount you return to player A. Player A will get the points she or he has kept plus the points you return to her or him. There will be only one round of this game.

Before you have to make your decisions on how many points to send to player A, we will show you the distribution of decisions of B players in an earlier, very similar version of this game. This game was performed with students at another university. The x-axis shows the proportion of points the B player returned to A. For example: if A sends 6 points to B, B receives 18 points. B returns 6 points. The proportion B returns is 6 / 18 = 33%. On the y-axis you see the percentage of players

corresponding to that proportion.

(Source: An investment game with third-party intervention, Charness et. al, 2008)

0 10 20 30 40 50 0-20% 20-40% 40-60% 60-80% 80-100% Per ce n tage o f p lay e rs Proportion returned to A

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Now, you have to decide how many points to send to A. Remember, these points are not tripled.

Game instructions (Player B – low treatment group)