The effect of punishment on cooperation in public good dilemmas with uncertainty about endowments Ori Weisel & Gary Bornstein Kyoto, August 2009

To implement uncertainty about endowments, variance is necessary. From which distribution are endowments drawn? Also – when are endowments drawn? Our decision – endowments are drawn from a commonly known distribution on every round. Experiment 1 -

To implement uncertainty about endowments, variance is necessary. From which distribution are endowments drawn? Also – when are endowments drawn? Our decision – endowments are drawn from a commonly known distribution on every round. Experiment 1 -

Punishment with individual uncertainty Method & Design – Experiment 1 & 2 Partner design 4-person groups endowments are sampled independently for each player on each round Contributions are doubled and divided equally among the 4 group members Exp 1,2: The game is repeated for 36 rounds First 18 rounds without punishment Last 18 rounds with punishment Exp 3: The game is repeated for 72 rounds First 36 rounds without punishment Last 36 rounds with punishment (Participants do not know number of rounds, nor that there will be a punishment stage)

2 treatments depending on the feedback following each round: Private information Only the number of points contributed by each of the other 3 players. Public information Also the number of endowment points available to each of the other players.

Punishment Following feedback, each participant could use up to 5 (exp. 1,2) or 24 (exp. 3) points to punish one other group member. Each point cost the punished player 3 points.

Exp 1 (Uniform distribution) – Contribution rates

Exp 1 (Uniform distribution) – Efficiency

Exp 2 (Normal distribution) – Contribution rates

Exp 2 (Normal distribution) – Efficiency

Exp 1 (Uniform distribution) Exp 2 (Normal distribution) Contribution. rate Efficiency

P=0.25 P=0.50 P=0.75 Contribution rates Efficiency

Exp 1 (Uniform distribution) – Public – Who punishes who?

Exp 1 (Uniform distribution) - Private – Who punishes who? ns ns ns ns

Exp 2 (Normal distribution) - Public – Who punishes who? ns ns s s

Exp 2 (Normal distribution) - Public – Who punishes who? ns ns ns ns

Exp 1 (Uniform distribution) - Who punishes who Exp 1 (Uniform distribution) - Who punishes who? - Exp 2 (Normal distribution) Public Private

Exp 3 (Binary) - Who punishes who?

Exp 1 (Uniform distribution) – Contribution rate per endowment level

Exp 2 (Normal distribution) – Contribution rate per endowment level

Contribution rate per endowment level Exp 1 (Uniform distribution) Contribution rate per endowment level Exp 2 (Normal distribution)

Within group payoff variance For each group member, we computed the overall payoff with and without punishment. For each group, we computed the variance of group member payoffs. Y axis - The mean of these variances.

Within group payoff variance For each group member, we computed the overall payoff with and without punishment. For each group, we computed the variance of group member payoffs. Y axis - The mean of these variances.

Within group payoff variance For each group member, we computed the overall payoff with and without punishment. For each group, we computed the variance of group member payoffs. Y axis - The mean of these variances.

Conclusion Punishment mechanisms may be very effective in enhancing cooperation when full information is available But They are less effective – and may be destructive – when information is incomplete and free rider detection is problematic.

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