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

2. 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 -

3. 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 -

5. 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)

6. 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.

7. 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.

8. Exp 1 (Uniform distribution) – Contribution rates

9. Exp 1 (Uniform distribution) – Efficiency

10. Exp 2 (Normal distribution) – Contribution rates

11. Exp 2 (Normal distribution) – Efficiency

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

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

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

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

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

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

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

19. Exp 3 (Binary) - Who punishes who?

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

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

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

23. 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.

24. 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.

25. 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.

26. 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.

27. end