Reaching Cooperation: A Pilot Study Comparing Formal and
Informal Punishment in a Public Goods Game with Heterogeneous Agents
15-12-2014
Marieke van der Wilt
6076939
MSc Economics – Behavioural Economics and Game Theory
Faculty of Economics and Business
Universiteit van Amsterdam
Under supervision of Matthias Weber
Second Examiner: Joep Sonnemans
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1.
Introduction
Reaching cooperation in situations with conflicting personal and common interests has been a long known challenge to humanity. Therefore, the potential solution to this problem has been extensively discussed and overthought. In Thomas Hobbes’ Leviathan, written during the English civil war, Hobbes discusses the use of social contracts as a necessity to prevent the human state of nature. According to Hobbes, this is a state of war of all against all. Hobbes argues that “[T]here must be some coercive power to compel men equally to the performance of their covenants by the terror of some punishment greater than the benefit they expect by the breach of their covenant […]” (Hobbes & Gaskin, 1998). Since the 17th century, western societies have progressed and, inevitably, so have the cooperation problems the western world faces. However, the argument Hobbes makes is still as applicable as it was back then. From the provision of public goods, to small scale cooperation in teams or companies; in order to prevent freeriding, it is essential to create a mechanism in which cooperation has a higher payoff than freeriding. As was concluded by Hobbes, a potential way to decrease the attractiveness of freeriding is punishment.
In public goods games performed in experimental settings, it has indeed been found that punishment can increase cooperation levels (Fehr & Gächter, 2000). Another factor that has been shown to increase cooperation in public games is endogenous choice, which involves subjects to choose how punishment is organized (Walker et al., 2000). Endogenous choice is often implemented in experiments through voting. Although punishment and endogenous choice have shown promising results with homogeneous agents, it appears more difficult to reach cooperation in groups with heterogeneous agents (Brick & Visser, 2012). The most important reason for this seems to be that subjects try to prevent being punished by only allowing punishment of other productivity types. This often leads to a situation without punishment. This is a problem, as many real life social dilemmas involve parties with different interests and productivities. More research is therefore needed to learn what can improve cooperation in heterogeneous groups.
This pilot study aimed at further studying cooperation in heterogeneous groups in a one-shot game with endogenous choice of punishment. It was studied whether the level of cooperation is influenced by the way in which punishment is carried out. Heterogeneity was created by having a high productivity type (A) and a low productivity (B) type. The experiment
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consisted of a formal and an informal treatment. In the formal treatment, subjects voted whether player types should be punished (for example: “below average contributing A type players”). If a majority within a group voted for a certain type, this type would be punished automatically after the contribution stage. In the informal treatment subjects voted in the same way, but punishment was not carried out automatically. After seeing the contributions of all players, participants could decide to pay for punishing another player if the voting stage allowed for this.From this pilot experiment it was concluded that subjects in the formal treatment were more likely to vote for punishment. Also they contributed more to the public good. Punishment was installed more often in the formal treatment, but this difference was not significant. Although this was a pilot experiment, and the results have limited statistical power, a centralized punishment system could potentially be a promising way to increase cooperation in heterogeneous groups. This is an interesting result, as previous experiments have shown there is often little cooperation in heterogeneous groups. A full-size study is needed to confirm the results of this pilot.
This thesis is structured as follows: In section 2 the related literature is discussed. Section 3 treats the experimental design and the hypotheses. Results can be found in section 4. Section 5 contains the conclusions and discussion.
2.
Related literature
Fehr and Gächter (2000) carried out one of the first experiments in which the effect of punishment in public goods games was studied. They studied homogeneous agents in a repeated interaction. The subjects had the opportunity to punish one another after getting to know each other’s contributions to the public good. This method substantially increased cooperation compared to mechanisms without punishment. During the same year, Walker et al. (2000) performed a study in which the effect of voting on cooperation in a common pool resources game with homogeneous agents was measured. It was found that cooperation increased when people could install a binding allocation rule through voting.
In the real world it is unlikely that people in a common pool resource dilemma have equal costs and benefits. Therefore, Margreiter et al. (2005) compared homogeneous groups and heterogeneous groups in an experiment similar to that by Walker et al. (2000). Although
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homogeneous groups performed as well as in the study by Walker et al. (2000), it appeared difficult for heterogeneous groups to reach agreement on allocations. It seems straightforward that differences in productivity and interests can complicate reaching agreement in heterogeneous groups. However, the experiment might have overstated the lack of agreement in heterogeneous groups. Subjects proposed allocations by indicating the exact number of tokens that every player would receive. An allocation was installed by majority vote, and if multiple proposals were the same, votes for the proposals were summed up. Subjects only had one vote, so the lower the amount of distinct proposals, the higher the chances of finding a majority, due to the lesser voting options. The odds of having similar proposals, and thus decreasing the number of distinct proposals, can be expected to be higher for the homogeneous group. Indeed, Margreiter et al. found that the number of different proposals on average was 3.6 for homogeneous groups and 4.7 for heterogeneous groups (2005). A different way of creating proposals could have lessened this advantage of homogeneous groups over heterogeneous groups in this experiment.Kroll et al. (2007) further investigated the effect of voting on cooperation, and applied it to public goods games. They compared non-binding and binding voting with and without punishment in a public goods game with homogeneous agents. It was found that non-binding agreements have a small and temporary effect on cooperation as long as no punishment is in place. Binding voting strongly increased contributions, and non-binding voting with punishment showed a similar, but slightly smaller, increase in cooperation. It was concluded that a combination of voting and punishment is required to decrease freeriding, and that voting alone has a small effect. Ertan et al. (2009) let homogeneous agents vote on whether, and what type of, punishment was allowed in a repeated voluntary contributions mechanism. The data show that initially subjects prevented punishment, but that eventually a situation developed in which only low contributors got punished. Participants had to choose whether or not to allow punishment of below average, average, and/or above average contributors. Subjects also chose whether or not they punished others if elections allowed for this. Unlike the system used by Margreiter et al. (2005), this voting system does not appear to benefit homogeneous groups more than heterogeneous groups. This system therefore seems more suitable to compare the extent of cooperation in heterogeneous and homogeneous groups.
Noussair and Tan (2011) adopt a slightly adjusted version of this voting system, and use it to study heterogeneous agents. Each group consists of two A type players with a high
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Marginal Per Capita Return (MPCR) and two B type players with a low MPCR. The only difference in the voting system with the one used by Ertan et al. (2009) is that voting for punishment of average contributors is no longer an option. The remaining options are therefore punishment of ‘high contributors’ and ‘low contributors’ for both player types. The reason to exclude the ‘average’ option was to limit the number of possible punishment systems that could be chosen. The results of the experiment show that the most efficient regimes in terms of welfare were the ones in which only low contributors were punished. However, few groups converged to this system. The main reason for this was that subjects tried to prevent punishment of their own type, and thus it was difficult to reach a majority in favour of punishment of a certain type. In order to lessen this effect, it might have been advantageous to keep the extra voting option used by Ertan et al. (2009). The availability of an ‘average’ option could psychologically decrease the perceived risk of being punished as ‘low contributor’, while actually contributing an almost average amount. If the only possibilities are low and high, the subject might find the risk of accidentally being in the ‘low group’ too high to vote for the punishment of low contributors.The previously mentioned studies all focused on ‘decentralized’ or ‘informal’ punishment. Subjects had to decide on an individual basis whether or not they wanted to target part of their earnings at punishing other subjects. An alternative for this punishment type is ‘centralized’ or ‘formal’ punishment, in which punishments are automatically executed by a central authority or by the group as a whole (Putterman et al., 2010). An argument in favour of the use of formal sanctions in economic experiments, is that formal sanctions are widely available in western societies. Informal sanctions, in which one person pays to decrease some other person’s income, appear less frequent. Formal sanctions were used in a study by Putterman et al. (2010), where subjects voted on whether a central authority should carry out punishment, and who should be punished. The experiment takes the form of a repeated public goods game with homogeneous agents. Most groups quickly reached the efficient outcome, in which only below average contributors to the public good receive punishment.
A lab-in-the-field study by Baldassarri and Grossman (2011) also involves centralized punishment in a repeated public goods game, and uses Ugandan farmers as homogeneous agents. Subjects vote on a representative, which has the power to punish. The authors compare cooperation under an elected representative and under a randomly chosen ‘punisher’, and find that cooperation is higher when the punisher is ‘legitimate’. However, any ‘punisher’ increases cooperation compared to the baseline without punishment.
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Markussen, Putterman & Tyran (2014) let homogeneous voters choose between informal-, formal- and no sanctions. Formal sanctions carried variable as well as fixed costs, of which the height varied over treatments. Although subjects were responsive to variations in the costs of formal sanctions, informal sanctions were chosen relatively often. If informal sanctions were endogenously chosen, earnings and contributions were 30% higher than when subjects did not choose themselves. The authors argue that a vote for informal sanctions might be perceived as signalling that without fixed costs subjects will still contribute substantial amounts. This could explain the success of informal sanctions in this experiment.Brick and Visser (2012) challenge that endogeneous choice has an effect on cooperation in heterogeneous populations. They carried out a framed public goods experiment with heterogeneous agents, who went through four treatments, in three different sequences. There was a baseline sequence and two voting sequences. The voting sequences included playing repeated games, and started with the baseline treatment. Next, a communication treatment, and two different types of tax treatments were played (the two voting sequences differed in order). Finally, there was a last round in which all subjects in the experiment voted which of the non-baseline treatments would be installed for the 5th round. Voting was based on a majority
vote of all subjects in the experiment. Interestingly, in both sequences, the sequence prior to voting was chosen by a majority. In one sequence this was the communication treatment, and in the other this was a tax treatment. It seems as if subjects were influenced by the treatment they last encountered. An explanation for this could be that they simply recalled this round best. Although multiple studies have shown the added value of endogenous institution choice on cooperation in a homogeneous population (Walker et al., 2000; Margreiter, Sutter & Dittrich, 2005; Baldassarri & Grossman, 2011), Brick and Visser conclude that endogenous choice does not have an effect on cooperation in heterogeneous populations. However, this study deviated in a number of ways from previous experiments, which found enhanced cooperation from endogenous choice with homogeneous agents. First, it was shown by Kroll, Cherry, & Shogren, (2007) that punishment should be available for endogenous choice to have an effect. This was not the case in the study by Brick and Visser (2012). Second, most previous experiments counted majority votes per group in the treatment, instead of over all subjects as in the experiment by Brick and Visser (2012). Third, the choice process in the experiment by Brick and Visser was more complex than that of other experiments. This might explain why the last encountered option received the majority of votes in both sequences.
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More research is required to determine how heterogeneous agents respond to different types of endogenous choice. This study contributes to the existing literature by studying cooperation in a public goods game with heterogeneous agents in two different treatments. In both treatments subjects vote whether a punishment system1 will be installed, but in one system subjects have to carry out punishment themselves (informal punishment), while in the other system a central authority automatically punishes (formal punishment). A pilot experiment is carried out with the purpose of answering the following question: “To what extentdoes sanction type influence cooperation in a public goods game in which heterogeneous agents vote on who should be punished?” Uncertainty of punishment and contributions by other
players is higher in a heterogeneous group than in a homogeneous group. An advantage of formal sanctions might be that it increases certainty and size of punishment. Therefore, this system might be especially attractive for heterogeneous agents, and cooperation is expected to be higher in the formal treatment.
3.
Experimental design
3.1 Experimental designThis experiment takes the form of a one-shot public goods game with heterogeneous agents. The design is largely based on that of Noussair and Tan (2011). A one-shot game was chosen for it allowed to distinguish effects from the different treatments without including an incentive to punish in order to increase future earnings. An advantage with respect to repeated games was that differences in punishment must result from differences between the treatments, as there are no future periods which influence strategies. A second advantage of the one-shot game was its appropriateness for a session with multiple short experiments (see Experimental setting below).
It could be argued that a disadvantage of choosing a one-shot game is that there is no financial incentive to punish in the informal treatment. However, Fehr and Gächter (2002) showed that “altruistic punishment” regularly takes place and improves cooperation in one-shot public goods games. The term altruistic punishment was created by Fehr and Gächter to
1 If a punishment system is installed at least one type of player is (allowed to be) punished. If no punishment system is elected, no punishment is possible in the public goods game.
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describe punishment for which there is no financial incentive (2002). As this type of punishment has been shown to occur, it is unlikely that the lack of repetition in this experiment will lead to an absence of punishment.Apart from the choice for a non-repeated game, two other deviations from the design by Noussair and Tan (2011) were made. First, as in Ertan et al. (2009) subjects have an extra voting option, which will be elaborated on below. Second, it is not possible to abstain from voting in this experiment2. In the experiment by Ertan et al. (2009) it was possible to abstain.
In this study a formal and an informal treatment are compared. Each of four subjects receives 10 tokens and decides whether to keep them all for himself, or whether to allocate any share to a common “project” (C). The exchange rate of tokens to euros was 1:0.5. Every group has two high productivity subjects (denoted as A type players), and 2 low productivity subjects (denoted as B type players). As in Noussair and Tan (2011), low production agents have a MCPR of 0.3 per token, and high production agents have a MCPR of 0.9 per token. This implies that per token invested in the public good by A type players (CA), all agents receive 0.9. For each token
invested by a B type player (CB), all agents receive 0.3 tokens. Earnings of subject i before
punishment (πib) can therefore be calculated as:
πib = (10 – C) + 0.9CA + 0.3CB
Punishment can occur in both treatments, but the two treatments differ in terms of how this is organized. In the formal treatment punishment is carried out by a central authority. Once subjects have voted for certain types to be punished, these types automatically receive punishment after the contribution stage of the public goods game. In the informal treatment, subjects vote on the subject types that are allowed to be punished. If a punishment system is installed, participants get the chance to punish the ones that qualify for punishment after the contribution stage of the public goods game. The voting procedure asks subjects which types of players should (be allowed to) receive punishment, as in Ertan et al. (2009). Subjects can choose any combination of the following possibilities (table 1), but can also decide not to vote for any
2 This choice was motivated by the will to keep the experiment as simple as possible. Although there was no official way to abstain in this experiment, it was possible not to vote for anything.
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punishment at all. If a majority (3 or more) votes for a certain type, this type qualifies for punishment. If no majority vote is reached, no punishment will occur.Table 1: Overview of voting options for punishment
In the informal treatment subjects must pay 1 token to deduct 3 tokens from another subjects’ earnings. Each subject can at most allocate 5 tokens to punish others, and punishment cannot exceed income3. In the formal treatment costs of punishment are 0.5 times total punishment, and these costs are evenly spread over the whole group. The ratio of collective costs to punishment in the formal treatment is therefore 1:34, just as in the informal treatment.
Therefore, the earnings after punishment of person i in the formal and informal treatment (respectively), can be described according to the following formulas:
πiformal = (10 – C) + 0.9CA + 0.3CB – 0.75Po – 6Pr
Where Po is the number of group members that received punishment, and Pr equals 1 if the
subject received punishment, and 0 if not.
πiinformal = (10 – C) + 0.9CA + 0.3CB – (Pp – 3Pr)
3 If punishment exceeds earnings, the punished subject’s earnings will be set to zero. 4
If punishment is 3, costs will be 0.5*3=1.5. These costs will be spread over all four subjects. Every subject pays 1.5/3=0.375. Total punishment will be 3+0.375=3.375. The other three players pay a total of
3*0.375=1.125, so the ratio of collective costs to punishment is 1.125:3.375=1:3.
Below average contribution (0 to average – 1) Average contribution (average – 1 to average +1) Above average contribution (average + 1 to 10) High MPCR (A type) Low MPCR (B type)
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Where Pp equals tokens of punishment the subject paid for, and Pr stands for tokens paid for byother group members to punish the subject.
3.2 Experimental setting
The experiment was conducted on computers of the Center for Research in Experimental Economics and Political Decision Making (CREED) lab of the University of Amsterdam. The experiments were part of two sessions organized for experiments by Master students of the Master in Behavioural Economics and Game Theory at the University of Amsterdam. In both sessions subjects were available for two hours in which they participated in seven different experiments. Students received a show-up fee of €7.00 and a lottery at the end of the session determined which of the seven experiments would be paid out.
The formal treatment was conducted during the morning session, and the informal treatment during the afternoon session. Both the formal and informal treatment lasted between 10 and 15 minutes. As there were 24 subjects per session, six groups per treatment were formed. Table 2 summarizes information about the subjects that participated in both sessions. All subjects were Dutch-speaking, and subjects that did not have an economics background came from a wide range of other fields, including humanities, social sciences and sciences.
Table 2: Summary of treatments and subjects
Formal treatment Informal treatment Overall
Number of subjects 24 24 48
Female (%) 29% 42% 35%
Economics major (%) 58% 38% 48%
Familiar with game theory (%) 54% 46% 50%
This was the fifth experiment which subjects encountered. Before the session started, subjects received general instructions. In these instructions subjects were informed that they would receive new instructions for every separate experiment. When this experiment began, students received the experiment-specific instructions on their computer as well as on paper. The experiment started as soon as all players indicated to be ready by selecting the “ready” option on their screen. In the formal treatment a control question was asked during the
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instructions. In the informal treatment there were no control questions. The first screen in both treatments indicated the subject’s player type. After this screen, subjects proceeded to the voting stage, in which they indicated whether or not they wanted certain player types to (be able to) receive punishment5. As soon as all group members had voted, the group continued to a screen showing the elected outcomes. After this screen, the second stage started and subjects entered their contributions to the public good. When all group members were ready, the group progressed to a screen reporting contributions and earnings. In the formal treatment, this screen included punishment, costs of punishment and earnings after punishment. In the informal treatment the screen contained space where subjects could enter a number of tokens (0 ≤ Pp ≤ 5) directed at punishment of other players. Subjects could only enter tokens for thosegroup members who were eligible for punishment as a result of the elections and their behaviour in the public game. After all group members were ready, subjects proceeded to a screen with earnings after punishment.
3.3 Predictions and hypotheses
The existence of multiple productivity levels, and thus multiple interests, is the main reason why it is difficult to reach agreement on punishment systems in heterogeneous groups. This is easily illustrated by coming up with two valid, but opposing, philosophies suggesting which player type should contribute more tokens. For example, A players might argue that total value from contributions to the group is most important (tokens contributed to public good x productivity). They would reason accordingly that B players should contribute more, in order to compensate for their low productivity6. An opposing argument from the perspective of B players could be that ‘cost’ of contribution is most important. This would suggest that A players should contribute more, because contributing is less costly for them7. The latter could be seen as a typical socialist argument that the strongest should contribute most.
5 A full overview of the screens can be found in the appendix 6
Following this line of reasoning a B player should always contribute three times as many tokens as an A player. If an A player contributes 3 tokens, value of this contribution per person is 3 x 0.9 = 2.7. In order for a B player to create a value of 2.7, he would have to contribute 9 tokens: 9 x 0.3 = 2.7.
7The costs of contribution to the public good could be seen as payoff of keeping the
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These are only two arguments, and, undoubtedly, more can be thought of. Regardless of what is the fairest way to allocate tokens, this illustrates the challenge faced by subjects participating in this experiment. In the voting stage of the public goods game subjects base their votes on their own views, their expectations of the views of the others, and perhaps even their expectations of the other subjects’ expectations. Based on their beliefs subjects will form a strategy and vote accordingly. As there are four players per group it is almost impossible to guess correctly what the exact strategies of the other players will be. It is therefore likely that subjects will choose a voting strategy that they consider to be the best in a number of different situations. As soon as the results from the vote are shown, subjects receive information about their group members’ preferences. After this, participants contribute based on their beliefs and strategy.Maximum welfare for the group as a whole is reached when all players contribute their full endowments to the public good and there is no punishment. However, the way in which individual subjects can reach maximum earnings depends on different factors, such as punishment and group members’ contributions. The fact that punishment differs in both treatments likely influences the decisions that are made in both treatments. Some predictions are described below that are specific for the two treatments.
Formal treatment
If a punishment system is installed and players match the types that qualified for punishment, punishment is carried out automatically. This influences the decision making process while voting, and could trigger the use of different strategies compared to those in the informal treatment. Described below are some key elements and their hypothesized effect on the voting outcomes in the formal treatment.
It can be expected that players desire a punishment system that increases earnings compared to a situation in which there is no punishment. This implies that expected earnings from additional contributions should outweigh costs of punishment. Installation of a punishment system could potentially increase
A player would be 0.1 (1 – 0.9 = 0.1), while costs of contribution would be 0.7 (1 – 0.3 = 0.7) for
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contributions and decrease freeriding. In general it is advantageous for subjects if group members contribute much to the public good8. Costs of punishment per group member are 0.75 for every group member that gets punished. In terms of payoff, installing a punishment system is only profitable for subjects that do not receive punishment themselves, if the expected increase in earnings from contributions is larger than the expected costs from punishment of others. The higher the number of player-types that qualify for punishment, the higher the chances that many will receive punishment, and thus costs of punishment will be high. It is therefore in the interest of subjects to limit the number of types that will receive punishment.Informal treatment
In the informal treatment punishment is more flexible than in the formal treatment. This means that subjects have the opportunity of posing the threat of punishment without actually punishing. Below are some key decision making elements and their hypothesised effect on the voting process in the informal treatment.
Installing punishment of certain types does not automatically lead to punishment and costs of punishment. This means that the voting decision of subjects in the informal treatment is likely less based on weighing future costs of punishment than in the formal treatment. For subjects in the informal treatment the voting decision is likely an assessment of the probability of increased earnings and the probability of receiving punishment. On the one hand, installing a punishment system might increase contributions. On the other hand, group members have a low predictability, and installing a punishment system implies a risk of getting punished. The size of punishment is dependent on the subjects’ group members, which adds an extra element of unpredictability. As in the formal treatment, it is likely that subjects want to find
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The only exeption being the one in which low contributers get punished, and a player underestimates the others’ contributions to such an extent that he unexpectedly becomes a below average contributor and thus receives punishment.
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a balance between risk and returns, and that they will limit the amount of punishment options. Since the punishment system is just a threat, but does not automatically lead to punishment, subjects will consider if this threat is realistic. From an earnings perspective it is irrational to punish in a one-shot setting, as it will diminish earnings without bringing any future benefits (as would be possible in a repeated game). Following this line of reasoning, it could be argued that the threat of punishment is non-credible. However, as previous experiments have shown that altruistic punishment occurs, the threat of punishment is realistic, and installing a punishment system can lead to increased contributions.
From the above differences between the treatments the following three hypotheses have been formed:
1. In the formal treatment groups will vote for and select punishment systems more often than in the informal treatment.
Subject in both treatments have an incentive to install a punishment system punishing low contributors in order to drive up contributions. However, there are three main factors that differ between the treatments. First, not all subjects might consider the threat of punishment credible in the informal treatment. If subjects do not consider punishment a credible threat they do not have an incentive to vote for a punishment system. Even if only a small share of subjects considers the threat non-credible, this might have an effect on voting outcomes. More people may therefore vote for punishment systems in the formal treatment than in the informal treatment.
Second, installing a punishment system in the informal treatment comes with higher uncertainty than in the formal treatment. It is uncertain whether group members will punish, but also what the size of punishment will be. In the informal treatment the event of losing all earnings after punishment is plausible, while in the formal treatment this is highly unlikely9. On
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In the formal treatment maximum punishment is 6, and costs of punishment are 0.75 per subject who receives punishment. In the unlikely, but not impossible, event that all group members receive punishment, total punishment + costs per person would be 6 + 0.75 x 4 = 9. For A type players 9 is the minimum income possible (if the subject contributes his full endowment, and no other contributions
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the other hand, there is a chance in the informal treatment that no punishment will occur, even if punishment is allowed. This means the uncertainty can work out positively or negatively for subjects in the informal treatment. Risk-averse subjects might not like that they do not know what to expect when a punishment system is installed. This might prevent those subjects from voting for a punishment system, even though they have the power to install a system in which only a certain type can receive punishment.Third, there is a cost difference between the treatments. In the formal treatment players know that there is a reasonable chance that punishment will occur if a punishment system is installed. The more types are included in the punishment system, the larger the likelihood of punishment(s). Therefore, subjects expose themselves to higher risks of punishment costs with every extra box they tick on the voting form. In the informal treatment subjects only carry costs as soon as they decide to punish. Regarding cost efficiency, there is an incentive for subjects in the formal treatment to be more selective in terms of voting for punishment than in the informal treatment.
Considering the above effects, subjects in the informal treatment might consider punishment a non-credible threat, and are exposed to higher uncertainty after installing a punishment system. These are two reasons why subjects in the informal treatment might tick fewer boxes than in the formal treatment, or refrain from ticking boxes at all. On the other hand, people in the formal treatment must weigh the potential costs of punishment and the potential increase from punishing multiple types. This provides an incentive to limit the number of boxes ticked, but not to refrain from ticking boxes at all. If only one person gets punished, other subjects pay 0.75. If as a result of the punishment scheme a high productivity player contributes 1 more than he would have without the punishment system, the benefits of the
are made). For a B type player the minimum possible income is 3, if the player contributes his full endowment and no other contributions are made. If this would occur and a system would be in place in which above average contributors got punished, it would be possible that a player loses his full income to punishment. However, these are unlikely events. In the informal treatment punishment can become high especially when multiple players decide to punish the same person. For example, if three players decide to pay 2 tokens for punishment, punishment will be 6 * 3 = 18. Maximum possible punishment would be 3 * 15 = 45. As punishments can get higher in the informal treatment, it is more probable that this situation would occur in the informal treatment.
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system are already larger than the costs for the non-punished subjects (0.9 – 0.75 = 0.15). If punishing low contributors indeed increases contributions of all players, it is therefore likely that punishing below average contributors will increase earnings for those who do not get punished.It is hypothesised that due to the above expectations, subjects in the formal treatment will tick more boxes than their counterparts in the informal treatment. As a result of this, it is expected that fewer groups will manage to install a punishment system in the informal treatment than in the formal treatment.
2. Average contributions to the project per group will be higher in the formal than in
the informal treatment.
As mentioned above, there might be subjects in the informal treatment that do not consider punishment a credible threat. For those subjects, this public goods game with punishment is equal to a public goods game without punishment. As discussed in the literature section of this paper, punishment often increases contributions in public goods experiments. If some subjects consider the informal treatment to be a public goods game without punishment, this would predict that they will contribute less than other subjects that do consider punishment a credible option. Another aspect which might influence contribution differences between the treatments is the higher expected presence of punishment systems in the formal treatment. The presence of subjects that do not consider punishment a realistic option, as well as a higher presence of punishment systems in the formal treatment will likely cause freeriding to be more abundant in the informal treatment. Average contributions per group are therefore expected to be higher in the formal treatment than in the informal treatment.
3. More subjects will receive punishment in the formal treatment
For the formal treatment, if a punishment system is in place, it is likely that punishment will occur. Since it is expected that some type of punishment system is installed in the formal treatment, it is probable that punishment will take place. In the informal treatment it is less likely that punishment will take place after a punishment system has been installed. Also it is expected that fewer groups in the formal treatment will install a punishment system. Therefore,
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it is hypothesised that more punishment will take place in the formal treatment. Punishment is measured as number of subjects punished per group in the treatment10.Furthermore, some general expectations about voting behaviour lead to the following hypotheses:
4. Subjects will not install punishment systems in which above average contributors
receive punishment.
Increasing earnings through increased contributions is expected to be the main reason for installing a punishment system. It is likely that only systems that punish below average contributors will succeed in increasing contribution levels without incurring high levels of punishment (costs). A combination of punishing below average and average contributors could drive up contributions even faster, but chances are that the costs of punishing average contributors will outweigh the additional earnings. This system only makes sense in a group with large difference in contributions, and in a one shot game there is no chance to learn more about contribution behaviour of group members. Thus there is no information which indicates whether or not the subject is in a group with strongly differing contributions. If a regime is in place in which average contributors receive punishment and all players contribute the same, everyone receives punishment (even if all players contribute their full endowment). This makes the system inefficient, as costs are incurred to all players. An alternative motivation for installing a punishment system, which would include punishing high contributors, is antisocial punishment. However, it is not expected that a majority within a subject group will vote for antisocial punishment. It is therefore hypothesised that groups will not install any punishment systems in which above average contributors (are allowed to) receive punishment.
5. Punishment systems that only punish low contributors are most efficient in terms of
earnings after punishment.
Punishing below average contributors is likely the best way to drive up earnings, without incurring high costs of punishment. In other studies with repeated public goods games the most
10 Another option would have been to measure total punishment (tokens subtracted from earnings). However, as punishment is variable in the informal treatment, this might over- or underrepresent one treatment, depending on the size of punishment in the informal treatment.
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efficient punishment system was indeed shown to be this system (Ertan, Page, & Putterman, 2009; Putterman, Tyran, & Kenju, 2010; Noussair & Tan, 2011). As described at hypothesis 4, punishment of average contributors might carry the advantage of driving up contributions to very high levels, due to fear of punishment. However, if contributions are similar there is a chance that the majority of the group receives punishment, which is costly and decreases welfare of the group as a whole. Punishment of high contributors decreases welfare of the group and does not bring any advantage in terms of driving up contributions. It will likely decrease contributions instead. It is therefore expected that groups who only punish below average contributors will have the highest welfare (total earnings after punishment).6. Players will try to prevent receiving punishment, by primarily voting for punishment of the other player type.
Noussair and Tan (2011) explained the lack of agreement in heterogeneous groups by the fact that subjects tried to prevent punishment of their own type. Because of this phenomenon, heterogeneous groups in the study by Noussair and Tan had difficulties reaching a majority in favour of a certain punishment system. As in Ertan et al. (2009), a voting option to punish ‘average’ contributors has been added in this study. This could decrease the perceived risk of unintentionally being a low contributor and receiving punishment when making a reasonable contribution. Although this measure has been taken, it can still be expected that subjects will show a tendency to vote on punishment of the other player type, rather than their own. It is expected that A players are more likely to vote for punishment of B players than B players are, and vice versa.
4.
Results
4.1 ResultsGeneral outcomes of the experiment are described in table 3. There is a notable difference between the number of times a punishment system was chosen among the two treatments. In the formal treatment only one group failed to agree on a punishment system, while in the informal group four out of six groups did not select a punishment system. For the analyses below a significance level of 10% was used, because of the small sample size. There was no significant difference in earnings between the treatments (U=16, p=.818).
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Table 3: Overview of punishment systems, contributions and earnings per treatmentInformal treatment Punishment system Number of times chosen
Average punishment in tokens Average contribution to public good Average earnings before punishment Average earnings after punishment11 Low B 1 16 4.75 16.35 12.35 Low A, B, Medium A 1 8 7.25 21.65 19.65 No punishment 4 0 3.69 15.84 15.84 Total 6 Weighted average 4 4.46 16.89 15.89 Formal treatment Punishment system Number of times chosen
Average punishment in tokens Average contribution to public good Average earnings before punishment Average earnings after punishment Low A, B 2 9 5.75 15.05 12.8 Low A, Medium A 3 12 6.83 20.37 17.37 No punishment 1 0 6.75 21.55 21.55 Total 6 Weighted average 9 6.46 18.79 16.54
The above table gives an overview of chosen punishment systems per treatment and corresponding punishment, contributions and earnings. ‘Punishment system’ indicates the player types that were eligible for punishment. ‘Number of times chosen’ indicates the number of groups in the treatment that chose this system. ‘Average punishment’ shows average punishment (including costs) per group per punishment system. ‘Average contribution to the public good’ indicates the average contribution per subject in the punishment systems. ‘Average earnings before’ and ‘after’ punishment indicate average earnings per subject per punishment system.
Conclusion 1: Subjects in the formal treatment voted for punishment systems more often than in the informal treatment, but did not install punishment systems significantly more often.
Subjects in the formal treatment ticked 2.21 boxes on average, while subjects in the informal treatment ticked 1.54 boxes on average. A Mann-Whitney test showed that this difference between the treatments was significant at 10% level and that subjects in the formal treatment were more likely to vote for some type of punishment (U=198, p=.052). In the formal
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Due to a mistake in the program, some earnings after punishment were not calculated properly. There were no questions about this, and it did not influence the outcomes of the experiment since all decisions had been made when the problem occurred.
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treatment five groups installed a punishment system, and in the informal treatment two groups did. Fisher’s exact test showed that this difference was not significant (p=.242).Conclusion 2: Contributions to the public good were higher in the formal than in the informal treatment.
On average, subjects in the formal treatment contributed 6.46 tokens to the public good, while subjects in the informal treatment contributed 4.46 tokens on average (see table 3). A Mann-Whitney test comparing averages per group in both treatments showed that at 10% level this difference was significant (U=6, p=.065). An overview of individual contributions, average contributions and earnings per group can be found in figure 1. Complete freeriding (contribution of 0 to the public good) occurred in four out of five groups without a punishment system and in one out of seven groups with a punishment system. The only complete freerider which was in a group with a punishment system was punished automatically (formal treatment, group 3).
Conclusion 3: There is no significant difference in the amount of punishment between the treatments.
There was more punishment in the formal treatment (punishment in five out of six, versus two out of six groups). Fisher’s exact test was executed to compare the number of punished subjects per group in both treatments. The difference between the treatments was not significant (p=.242).
Conclusion 4: Subjects did not install punishment systems that allowed for antisocial punishment.
Although five subjects (four in the informal treatment, one in the formal treatment) voted for punishment of above average contributors, high contributors were never included in elected punishment systems. Antisocial punishment did therefore not occur. As can be read from figure 2, the only types that were included in punishment systems (in various combinations) were Low A, Low B and Medium A. Medium B was never included. The punishment system that was selected most often was the one in which Low A and Medium A were punished, and B was never punished (three times in formal treatment). However, the
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Figure 1: Overview of contributions and earnings per groupFormal treatment
Informal treatment
Figure 1 provides an overview of individual contributions and earnings per group and per treatment. Each figure represents a group, and each title indicates whether a punishment system was installed, and if so, which type(s) were included in this system. All contributions and earnings are indicated in tokens. The average contribution of the group is displayed as an orange line.
Group 1 – no punishment
Group 5 – Below avg. A, Avg. A
Group 3 – Below avg. A, Below avg. B
Group 4 – Below avg. A, Avg. A
Group 2 – Below avg. A, Below avg. B
Group 6 – Below avg. A, Avg. A
Group 1 – No punishment Group 5 – Below avg. B Group 3 – No punishment Group 4 – No punishment Group 2 – No punishment Group 6 – B. avg. A, B. avg. B, Avg. A
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Figure 2 - Prevalence of player types in elected punishment systems0 1 2 3 4 5 6
Formal treatment Informal treatment
Below average contr. A type Below average contr. B type Average contr. A type
Figure 2 plots the number of times that different player types were included in different punishment systems. For example, the ‘below average contributing A player’ was punishable in 5 out of 6 groups in the formal treatment, and in 1 out of 6 groups in the informal treatment.
situation in which there was no punishment at all was seen even more often (once in formal treatment, four times in informal treatment). Interestingly, in the formal treatment the A type was included in punishment systems four times as often as B type players, while in the informal treatment the A type and B type were included as frequently.
Conclusion 5: The most efficient punishment systems were the ones in which not only below average contributors , but also medium A was punished.
It was predicted that as in previous research with repeated games the most efficient systems were the ones in which only below average contributors were punished. There was strong variation in the performance of groups without punishment over the treatments (see table 3). However, overall it seems that the most successful punishment systems were the two systems in which below average A as well as average A were punished (Below average A, Average A and Below average A, Below average B, Average A). The statistical significance of this finding is low due to the low number of observations.
Conclusion 6: Only in the informal treatment subjects were more likely to vote on the other player type to prevent punishment of their own type.
In order to test for the effect described by Noussair and Tan (2011), where subjects tried to prevent punishment of their own type, a Mann-Whitney test was performed. It was
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compared whether A type players were less likely to vote for punishment of B type players than B type players and vice versa. Over the entire population it appeared that A players were not less likely to vote for punishment of A players (U=245, P=.347), but B players were less likely to vote for punishment of B players (U=159, P=.004). When looking at the two treatments separately it appears that in the formal treatment there is no significant difference between voting behaviour of A type subjects and B type subjects (U=49.5, p=.198 and U=66.5, p=.755). In the informal treatment A type subjects were not significantly less likely to vote for punishment of A types than B types were (U=56, p=.378), but B types were less inclined to vote for punishment of B types than A types were (U=30.5, p=0.014).5.
Conclusion and discussion
This pilot study examined to what extent sanction type influences cooperation in a public goods game in which heterogeneous agents vote on punishment systems. The experiment compared a formal and an informal treatment. In both treatments subjects participated in a public goods game with punishment and three stages:
- A first stage in which subjects voted on whether a punishment system would be installed;
- A second stage in which the public goods game was played;
- A third stage in which punishment could be carried out depending on the outcome of stage one.
The two treatments differed in terms of how punishment was organized. In the formal treatment subjects voted on whether types would automatically be punished in stage three. In the informal treatment subjects decided which types were allowed to be punished in stage three, but the punishment decision had to be made by subjects themselves.
It was found that subjects in the formal treatment were more likely to vote for punishment and contributed more to the public good. Although subjects in the formal treatment also installed punishment systems more often, this difference was not significant. There was no significant difference between earnings in both treatments. In terms of earnings the most efficient punishment systems were the ones in which below average and average contributing A type players were punished. From these results the conclusion can be drawn that
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centralized punishment has potential to improve cooperation in heterogeneous groups, something that has been proven difficult in previous experiments. A full-size study is needed to confirm these results and to find out whether weakly significant results are still significant in a larger subject pool.This study had some shortcomings, most of which could be solved in a larger scale experiment. Due to the small sample size, the results have limited statistical significance. Also the fact that the experiment was part of a two-hour session in which subjects participated in a total of seven experiments has a drawback. For participating subjects the chance of receiving earnings from this specific experiment was only one out of seven. Although there were no signs of it, this might have caused subjects to pay less attention to the instructions and overall assignment. Only one question was asked, while subjects had limited time to go through two pages of instructions. Furthermore it would have been interesting to play multiple one-shot games to see what would happen if subjects had the chance to learn.
In this study a one-shot game was used. This has the advantage that there is little noise, because the results are not influenced by strategies concerning future rounds. However, it remains to be studied how cooperation in both different treatments develops in a repeated interaction. In the real world both repeated and one-shot cooperation problems are abundant, and it is therefore important to also study how both treatments perform in a repeated game. By fully understanding how cooperation in heterogeneous groups can be triggered through voting systems, it is possible to further improve cooperation in real world social dilemmas.
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Appendix 1 – Instructions formal treatmentThis experiment will last for approximately 15 minutes (including instructions). Your earnings will be calculated in tokens. The tokens will be converted to euros at the end, using the exchange rate 10 tokens = 1.50 euros (if you end up with a negative number of tokens you will receive 0 euros). If you have any questions, please raise your hand and someone will come to your desk!
All participants will be divided into groups of four. Each group consists of two type A players and two type B players. The computer will assign your type (A or B) to you. This experiment consists of two decisions, an allocation decision and a deduction decision.
Allocation decision
All group members receive 10 tokens. You and the other group members simultaneously decide how to allocate the tokens. You have two options:
Contributing tokens to a project
Keeping tokens in a personal account
You decide how many of the 10 tokens you want to contribute to the project, the rest is automatically allocated to your personal account (you can only contribute integer numbers, no decimals).
Your income consists of two parts:
The tokens in the personal account
Income from the project. For each token a type A player contributed to the project you receive 0.9 tokens. For each token a type B player contributed to the project you receive 0.3 tokens.
Example 1:
You are a type A player. You decided to contribute 5 tokens to the project. The other three players contributed 10 tokens each. Your income from the allocation decision will consist of the following parts:
5 tokens (that you have kept in the personal account)
13.5 tokens (= 0.9 * 15 tokens, received from the contributions of A players) 6 tokens (= 0.3 * 20 tokens, received from the contributions of B players) Thus, in sum your income is 24.5 tokens.
Deduction decision
Before the allocation decision, you can vote on whether you want tokens to be deducted (this means taken away) from participants after the allocation decision. The votes are conditional on how many tokens players contribute to the project, for A players and B players separately. You will vote by ticking boxes in a table as this one:
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Player typeContributions to the project low
(below “average -1”)
medium
(at least “average -1”, no more than “average + 1”)
high
(above “average + 1”) A
B
All four participants of your group decide on which of these six boxes to tick. If a box is ticked by at least three participants the deduction for players in the corresponding category will take place.
After the deduction decision and before the allocation decision, all participants will be told which deductions will take place (i.e., which boxes have been ticked at least three times). After the allocation decision, each participant falls into one of the six categories (depending on player type and contribution). If the box of a participant’s category had been ticked at least three times, 6 tokens will be deducted from this participant and an additional 0.75 tokens will be deducted from all players.
Example 2:
Participants are asked for their vote on the deduction decision. One of the A players ticks all six boxes. The other A player ticks none of the boxes. Both B players tick the two boxes in the first column of the table.
All participants of the group are told that the deduction takes place for A and B players who contributed a low number of tokens to the project, i.e. less than the average contribution of all players minus one (only these two boxes have been ticked at least three times).
Participants are asked for their allocation decision. Both A players and one B player contribute 8 tokens to the project. The other B player contributes 6 tokens. Incomes before any deductions are then (calculated as in Example 1):
A player 1 (8 token contribution): 20.6 (calculation: 2 + 16 * 0.9 + 14 * 0.3) A player 2 (8 token contribution): 20.6 (calculation: 2 + 16 * 0.9 + 14 * 0.3) B player 1 (8 token contribution): 20.6 (calculation: 2 + 16 * 0.9 + 14 * 0.3) B player 2 (6 token contribution): 22.6 (calculation: 4 + 16 * 0.9 + 14 * 0.3)
The average contribution is 7.5 (8 + 8 + 8 + 6 = 30, and 30 / 4 = 7.5). In this example the deduction takes place for A or B players that contributed less than the average contribution minus one, i.e. 6.5. Thus, there will be a 6 token deduction from the B player that contributed 6 tokens, and an additional deduction from all players of 0.75 tokens. Final earnings are thus: A player 1 (8 token contribution): 20.6 – 0.75 = 19.85
A player 2 (8 token contribution): 20.6 – 0.75 = 19.85 B player 1 (8 token contribution): 20.6 – 0.75 = 19.85 B player 2 (6 token contribution):22.6 – 6 – 0.75 = 15.85
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Appendix 2 – Instructions informal treatmentThis experiment will last for approximately 15 minutes (including instructions). Your earnings will be calculated in tokens. The tokens will be converted to euros at the end, using the exchange rate 1 tokens = 0.50 euros (if you end up with a negative number of tokens you will receive 0 euros). If you have any questions, please raise your hand and someone will come to your desk!
All participants will be divided into groups of four. Each group consists of two type A players and two type B players. The computer will assign your type (A or B) to you. This experiment consists of two decisions, an allocation decision and a deduction decision.
Allocation decision
All group members receive 10 tokens. You and the other group members simultaneously decide how to allocate the tokens. You have two options:
1. Contributing tokens to a project 2. Keeping tokens in a personal account
You decide how many of the 10 tokens you want to contribute to the project; the rest is automatically allocated to your personal account (you can only contribute integer numbers, no decimals).
Your income consists of two parts:
1. The tokens in the personal account
2. Income from the project. For each token a type A player contributed to the project you receive 0.9 tokens. For each token a type B player contributed to the project you receive 0.3 tokens.
Example 1:
You are a type A player. You decided to contribute 5 tokens to the project. The other three players contributed 10 tokens each. Your income from the allocation decision will consist of the following parts:
5 tokens (that you have kept in the personal account)
13.5 tokens (= 0.9 * 15 tokens, received from the contributions of A players) 6 tokens (= 0.3 * 20 tokens, received from the contributions of B players) Thus, in sum your income is 24.5 tokens.
Deduction decision
Before the allocation decision, you can vote on whether you want the possibility to deduct (this means take away) tokens from participants after the allocation decision. The votes are conditional on how many tokens players contribute to the project, for A players and B players separately. You will vote by ticking boxes in a table as this one:
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Player typeContributions to the project low
(below “average -1”)
medium
(at least “average -1”, no more than “average + 1”)
high
(above “average + 1”) A
B
All four participants of your group decide on which of these six boxes to tick. If a box is ticked by at least three participants deductions for players in the corresponding category will be possible. After the deduction decision and before the allocation decision, all participants will be told which deductions will be possible (i.e., which boxes have been ticked at least three times).
After the allocation decision, each participant falls into one of the six categories (depending on player type and contribution). If the box of a particular participant’s category had been ticked at least three times, it is possible for the other participants to pay tokens to deduct tokens from this participant. Per token paid 3 tokens will be deducted from the participant. You can at most use 5 tokens for deduction purposes.
Example 2:
Participants are asked for their vote on the deduction decision. One of the A players ticks all six boxes. The other A player ticks none of the boxes. Both B players tick the two boxes in the first column of the table.
All participants of the group are told that it will be possible to deduct tokens from A and B players who contributed a low number of tokens to the project, i.e. less than the average contribution of all players minus one (only these two boxes have been ticked at least three times).
Participants are asked for their allocation decision. Both A players and one B player contribute 8 tokens to the project. The other B player contributes 6 tokens. Incomes before any deductions are then (calculated as in Example 1):
A player 1 (8 token contribution): 20.6 (calculation: 2 + 16 * 0.9 + 14 * 0.3) A player 2 (8 token contribution): 20.6 (calculation: 2 + 16 * 0.9 + 14 * 0.3) B player 1 (8 token contribution): 20.6 (calculation: 2 + 16 * 0.9 + 14 * 0.3) B player 2 (6 token contribution): 22.6 (calculation: 4 + 16 * 0.9 + 14 * 0.3)
The average contribution is 7.5 (8 + 8 + 8 + 6 = 30, and 30 / 4 = 7.5). In this example participants can deduct tokens from A or B players that contributed less than the average contribution minus one, i.e. 6.5, which only includes B player 2.
Both A players decide to pay 1 token to deduct the tokens from B player 2. B player 1 decides not to pay to deduct tokens from B player 2. Final earnings are thus:
A player 1 (8 token contribution): 20.6 – 1 = 19.6 A player 2 (8 token contribution): 20.6 – 1 = 19.6 B player 1 (8 token contribution): 20.6
