Counter-punishment in Public Good Games

This is a lab experiment with a within-subjects design. We are replicating one of the treatment combinations -- the one that produces the key results -- from the original study. The original study has many additional control conditions, which we are not testing. Our replication consists of the control condition and the most extreme intervention included in the original study, and is conducted in a single order: Control then intervention, as described below. The original study tests for order effects, and we do not replicate that part of their study.

Subjects are randomly assigned into groups and play finitely repeated public good game for 20 periods: ten periods for the control condition followed by ten periods of the intervention. Groups are reformed each period randomly.

Subjects are randomly assigned into groups and will play the control game (the voluntary contribution mechanism (VCM)), and the treatment (counter-punishment (PCP)). We will compare the results of control and treatment interventions considering a within-subjects design.

The first intervention is the control condition is the the standard public good game, also known as the voluntary contribution mechanism (VCM), which has been conducted hundreds of times in many studies. In the game a subject is assigned to a group, and given an endowment. The endowment can be "kept" in personal earnings, or it can be "allocated" to a group account which is then used to produce the public good. The public good generates benefits (earnings) for all members of the group. The tension in this game is between individual maximizing behavior (keep all the endowment and free ride on others' allocations to the group account) and the social welfare (contribute all to the group account which maximizes total earnings of the group). This game is conducted for ten rounds.

The intervention is then implemented for the second ten rounds of the game. The intervention is the introduction of punishment. Punishment is two-sided – that is, a VCM followed by a stage of punishment and a stage of counter-punishment (PCP). In the punishment phase, any subject in a group can, at a personal cost, pay part of their own earnings to reduce the earnings (punish) another subject. The idea here is that contributors may punish free riders, leading to higher future contributions. In the counter punishment phase, those who punished others can be counter-punished by those whose earnings were reduced.

The key comparison is a paired statistical test between the play in the first ten periods and in the second ten periods.

2018-12-03

2019-12-31

Contribution level, earnings, welfare

Contribution level is the amount allocated to the group account in the first ten rounds, and in the second ten periods by individual.
Earnings is the earnings level for the first ten periods, and in the second ten periods, by individual.
Welfare is earnings for the first ten periods, and earnings net of punishment costs for the second ten periods.

Description of the Experiment
We will recruit 20-24 participants in each session of the experiment. Each session will last 1 hour and 45 minutes. In each session, we will divide the participants in five or six groups of four. We will analyze two treatments: voluntary contribution mechanism (VCM) and two-sided punishment (PCP). The participants will play ten rounds of VCM and ten rounds of PCP. At the beginning of each round, we will randomly assigned participants to a group and they will receive an endowment of 20 Experimental Currency Units (ECU). VCM consists of deciding how much to allocate from the endowment to a private account and a public account. At the end of each round, participant earnings which is given by the following formula:
[(Endowment-Contribution to public account) + 0.4*Total contribution of the group to public account].
Each round agents will decide how much to keep and how much to allocate to the group account. Each round they learn their own earnings, and so can infer the aggregate contributions of their group, but they will not know anything about the individual contributions of the other group members. We will inform participants in advance of how we will calculate their income in each round. After the ten rounds of VCM, participants will make decisions under PCP for other ten rounds. In each round, we will randomly assigned them to a new group. PCP consists of three stages per round:
1. At the beginning of this stage, agents will receive a 25 ECUs one-off lump sum payment that they can use at the end of the ten rounds to pay for eventual losses during this treatment. This lump sum payment is not considered when calculating the income of the round. Participants will receive a 20 ECU endowment to split between the public account and the private account. Then, we will inform them about their income [(Endowment of ECUs – Own contribution to the project) + 0.4*Total contribution tothe project]. This stage is similar to VCM plus the one-off lump sum payment.
2. In this stage, we will inform participants of each group member contribution to the public project in the first stage. Participants will have the opportunity to punish their teammates. They can reduce or leave equal the income of each member of the group by distributing points. Participants will choose points to assign to each group member. If a participant chooses zero points for a particular member, then the other member’s income will not change. However, each point assigned to a member reduces her income by 10%. Therefore, if a member receives 10 points or more, her income from the first stage will be reduced by 100%. However, each point distributed to another member has a cost in ECUs. Participants can distribute between 0 to 10 points to each group member. The more points a participant gives to any group member, the higher the costs. The total costs for each participant will be the sum of the costs of distributing points to each of the other three group members. The total income from stage 2 is as follows:
Total income at the end of stage 2 = (Income from the stage 1)*[1 – (1/10)*received points] – cost of distributed points
This total income can be negative if the cost of distributed points is higher than the income in the first stage. If agents have zero or negative income at the end of this stage, they will not be allowed to continue to the third stage.
3. In this stage, agents will be informed about the points that the other group members assigned to them in the second stage. They will have the opportunity of assigning points back to the other participants to reduce their income. A participant can only assign counter-points to those participants who assigned points to her in the previous stage. Each point assigned to another participant will reduce her income by 10% and the cost of each point will be the same as in stage 2. The cost of assigning points is cumulative. For example, if a participant distributes 2 points in the second stage to another participant, she will face a cost of 2 ECUs in the second stage. If in period 3 she decides to distribute 3 more points to the same participant, then the total cost in stage 3 is 9 ECUs. The total income from stage 3 is as follows:
Total income at the end of stage 3 = (Income from the stage 2)*[1 – (1/10)*received points] – total cost of distributed points
If participants make a negative income in stages 2 or 3, they will pay us back with the 25 ECU they received as a lump-sum payment. At the end of the experiment, we will calculate the total income participants made in the 20 rounds. If they made a total negative income in some rounds, they should pay us back with the 25 ECUs they received as a lump-sum payment. We will convert the total income to dollars and those will be their earnings of participating in the experiment, plus the show-up fee.

Randomization is done by the computer. Individuals are randomly assigned to groups, and re-grouped each round.

individual.

No

N/A

40 subjects with 20 periods each in a within-subject design.

N/A

using the allocation decision as the observation