Nobuyuki Takahashi (Hokkaido University) Ryoichi Onoda (Hokkaido University)

1. ICSD2009Kyoto The effect of common knowledge– Why do people cooperate more when they face a social dilemma situation where mutual cooperation yields restoration of fairness? Nobuyuki Takahashi (Hokkaido University) Ryoichi Onoda (Hokkaido University) Hikaru Hamada (Hokkaido University) Rie Mashima (Kumamoto Gakuen University) E-mail: ntakahas@let.hokudai.ac.jp

2. Introduction There have been many collective behaviors in human history. Collective behaviors seem to be thrived when the purpose is the restoration of fairness (e.g., civil rights movements, anti-Vietnam War movements). Why? Many collective behaviors involve social dilemmas. So, isn’t free-riding still the better option than participating in a social movement?

3. Takezawa (1999) 1) Experience of unfairness invokes the sense that unfairness is shared among the other people. 2) The goal changes from pursuing self-interest to jointly restoring fairness. 3) Expectation of others’ cooperation in one-shot public goods game (PGG) < Provision of PG restores fairness Ordinary one-shot PGG Since expectation of others’ cooperation promotes cooperation, 4) Cooperation rate < Provision of PG restores fairness Ordinary one-shot PGG Why does the experience of unfairness promote expectation of others’ cooperation?

4. Takezawa (1999) According to Takezawa (1999)… • The sense of fairness activates the common knowledge that everybody was treated unfairly. • This common knowledge induces higher level of expectation that leads to higher level of cooperation. Taken for granted, but… Why does this process occur? Why is the expectation of others’ cooperation higher when participants were all treated unfairly?

5. Fear of greed Fear of fear What is the function of being treated unfairly? What affects expectation? Two reasons to defect in SD(e.g., Dawes et al. 1986; Van Lange et al. 1992; Yamagishi & Sato 1986) (1) Greed – the temptation to free-ride (2) Fear – the prospect that one's cooperation may be exploited • Not greed but fear affects expectation of others’ cooperation. • However, there can be at least two sources of fear.

6. Revisiting Takezawa (1999) What is the function of being treated unfairly? Two possibilities (1) Reduction of fear of greed – People expect that the experience of unfairness transforms the goal of other people from maximizing self-interest to achieving mutual cooperation in order to restore fairness. We want to restore fairness! The other people will cooperate because they are no longer greedy. In order for the expectation of others’ cooperation to increase, in addition to reduction of fear of greed of the other players, reduction of fear of fear may be necessary.

7. However, this may not be sufficient to induce cooperation. But the other people may still defectbecause of fear. Fear of fear Revisiting Takezawa (1999) What is the function of being treated unfairly? Two possibilities (1) Reduction of fear of greed – People expect that the experience of unfairness transforms the goal of other people from maximizing self-interest to achieving mutual cooperation in order to restore fairness. We want to restore fairness! In order for the expectation of others’ cooperation to increase, in addition to reduction of fear of greed of the other players, reduction of fear of fear may be necessary.

8. Revisiting Takezawa (1999) (2) Reduction of fear of fear – Perception of unfairness makes people expect that the other people’s fear of greed was reduced. The others are no longer greedy! The other people will cooperate because they have no fear. Reducing fear of fear requires that the fact that everyone was treated unfairly is a common knowledge.

9. Main purpose of the study To differentiate these two functions and see if reduction of fear of fear is necessary for inducing higher level of cooperation • Reduction of fear of greed: Privately knowing that everybody was treated unfairly is enough • Reduction of fear of fear: The fact that everybody was treated unfairly must be a common knowledge Manipulation: Whether or not the fact that everybody was treated unfairly is a common knowledge

10. Experiment One factor, between-subjects design Participants : 125 undergraduate students (M: 68, F: 56, UK: 1) 1) Control condition : Ordinary one-shot PGG without any context 2) Common knowledge condition : One-shot PGG that is identical with Control condition. However, before playing the game, participants were all treated unfairly by a dictator and they could restore fairness by achieving mutual cooperation in PGG. 3) Private knowledge condition : The same as Common knowledge condition. The only difference is that only the participants knew that everybody was treated unfairly by a dictator, and that they could restore fairness by achieving mutual cooperation in PGG.

11. 1) Control condition • Ordinary one-shot PGG without any context • 1st stage: Social inference task (a bogus task) • Each player was paid 500 yen ($5) for completing the task. Social inference task 500 yen 500 yen 500 yen 500 yen 500 yen

12. 1) Control condition • Ordinary one-shot PGG without any context • 2nd stage: One-shot step-level PGG Cooperation : Provide 500 yen to the groupDefection : Keep 500 yen for oneself 500 yen 500 yen 500 yen 500 yen 500 yen If more than 3 players cooperate,

13. 1) Control condition • Ordinary one-shot PGG without any context • 2nd stage: One-shot step-level PGG Cooperation : Provide 500 yen to the groupDefection : Keep 500 yen for oneself 500 yen 4000 yen If more than 3 players cooperate, a public good (4000 yen) is provided.

14. 1) Control condition • Ordinary one-shot PGG without any context • 2nd stage: One-shot step-level PGG Cooperation : Provide 500 yen to the groupDefection : Keep 500 yen for oneself C C C C D 800 yen 500 yen 800 yen 800 yen 800 yen 800 yen 4000 yen Total earnings of cooperators : 500-500+(4000/5)=800 yen defectors : 500-0+(4000/5)=1300 yen

15. 1) Control condition • Ordinary one-shot PGG without any context • 2nd stage: One-shot step-level PGG Cooperation : Provide 500 yen to the groupDefection : Keep 500 yen for oneself 500 yen 500 yen 500 yen 500 yen 500 yen If less than 4 players cooperate,

16. 1) Control condition • Ordinary one-shot PGG without any context • 2nd stage: One-shot step-level PGG Cooperation : Provide 500 yen to the groupDefection : Keep 500 yen for oneself 500 yen 500 yen 500 yen 0 yen If less than 4 players cooperate, a public good is not provided.

17. 1) Control condition • Ordinary one-shot PGG without any context • 2nd stage: One-shot step-level PGG Cooperation : Provide 500 yen to the groupDefection : Keep 500 yen for oneself 500 yen 500 yen 500 yen Deception Although participants were told that there were other participants and that they would interact with them, actually each participant behaved as an individual. In other words, there was no real interaction among the participants. 0 yen If less than 4 players cooperate, a public good is not provided.

18. 2) Common knowledge condition • Identical incentive structure with the one in the other 2 conditions • 1st stage: Social inference task (a bogus task) • As a 6-person group, players were paid 7000 yen ($70) for completing the task. 7000 yen Social inference task

19. 2) Common knowledge condition • Identical incentive structure with the one in the other 2 conditions • After 1st stage (before 2nd stage): Dictator game • A dictator was chosen randomly from the group and decided to allocate 7000 yen among group members. Recipient Recipient Recipient Recipient Recipient ? yen ? yen ? yen ? yen ? yen Dictator Participant 7000 yen

20. 2) Common knowledge condition • Identical incentive structure with the one in the other 2 conditions • After 1st stage (before 2nd stage): Dictator game • A dictator was chosen randomly from the group and decided to allocate 7000 yen among group members. Since we used deception, however, actually a dictator and the other recipients did not exist. Only a participant was a real person. Also, dictator’s decision was predetermined by the experimenter. Recipient Recipient Recipient Recipient Recipient ? yen ? yen ? yen ? yen ? yen Dictator Participant 7000 yen

21. 2) Common knowledge condition • Identical incentive structure with the one in the other 2 conditions • After 1st stage (before 2nd stage): Dictator game • A dictator was chosen randomly from the group and decided to allocate 7000 yen among group members. The dictator allocated 4500 yen for himself and 500 yen for each of the other 5 players. Recipient Recipient Recipient Recipient Recipient 500 yen 500 yen 500 yen 500 yen 500 yen Dictator Participant 4500 yen

22. 2) Common knowledge condition • Identical incentive structure with the one in the other 2 conditions • 2nd stage: One-shot step-level PGG to restore fairness • 5 recipients were asked if they want to provide 500 yen. Cooperation : Provide 500 yen to the groupDefection : Keep 500 yen for oneself 500 yen 500 yen 500 yen 500 yen 500 yen Dictator 4500 yen

23. 2) Common knowledge condition • Identical incentive structure with the one in the other 2 conditions • 2nd stage: One-shot step-level PGG to restore fairness 500 yen 500 yen 500 yen 500 yen C C C C D 500 yen Dictator If more than 3 recipients cooperate, 4500 yen

24. 2) Common knowledge condition • Identical incentive structure with the one in the other 2 conditions • 2nd stage: One-shot step-level PGG to restore fairness C C C C D 500 yen Dictator If more than 3 recipients cooperate, 4000 yen was forfeited from the dictator, 500 yen 4000 yen

25. 2) Common knowledge condition • Identical incentive structure with the one in the other 2 conditions • 2nd stage: One-shot step-level PGG to restore fairness 4000 yen 500 yen Dictator If more than 3 recipients cooperate, 4000 yen was forfeited from the dictator, and recipients share 4000 yen equally. 500 yen

26. 2) Common knowledge condition • Identical incentive structure with the one in the other 2 conditions • 2nd stage: One-shot step-level PGG to restore fairness Total earnings of cooperators : 500-500+(4000/5)=800 yen defectors : 500-0+(4000/5)=1300 yen C C C C D 800 yen 800 yen 800 yen 500 yen 800 yen 800 yen Dictator If more than 3 recipients cooperate, 4000 yen was forfeited from the dictator, and recipients share 4000 yen equally. 500 yen

27. 2) Common knowledge condition • Identical incentive structure with the one in the other 2 conditions • 2nd stage: One-shot step-level PGG to restore fairness D D C C D 500 yen 500 yen 500 yen If less than 4 recipients cooperate, nothing happens. Dictator 4500 yen Total earnings of cooperators : 500-500=0 yen defectors : 500-0=500 yen

28. 3) Private knowledge condition • Identical with Common knowledge condition • The only difference is that participants are the only one who knew that everybody was treated unfairly. • After the dictator allocated 7000 yen, each player received an allocation sheet that only says how much she was allocated by the dictator. Recipient Recipient Recipient Recipient Recipient 500 yen ? yen ? yen ? yen ? yen Dictator ? yen

29. 3) Private knowledge condition • Identical with Common knowledge condition • The only difference is that participants are the only one who knew that everybody was treated unfairly. • After the dictator allocated 7000 yen, each player received an allocation sheet that only says how much she was allocated by the dictator. Recipient Recipient Recipient Recipient Recipient 500 yen ? yen ? yen ? yen ? yen Dictator ? yen By lottery one player was chosen as a person who could see the complete distribution of 7000 yen.

30. 3) Private knowledge condition • Identical with Common knowledge condition • The only difference is that participants are the only one who knew that everybody was treated unfairly. • After the dictator allocated 7000 yen, each player received an allocation sheet that only says how much she was allocated by the dictator. • The recipient who was chosen by lottery knew that the other recipients did not have full information. • She knew that she was the only person who knew how much each person received from the dictator. Recipient Recipient Recipient Recipient Recipient 500 yen 500 yen 500 yen 500 yen 500 yen Dictator 4500 yen By lottery one player was chosen as a person who could see the complete distribution of 7000 yen.

31. 3) Private knowledge condition • Identical with Common knowledge condition • The only difference is that participants are the only one who knew that everybody was treated unfairly. • After the dictator allocated 7000 yen, each player received an allocation sheet that only says how much she was allocated by the dictator. • The recipient who was chosen by lottery knew that the other recipients did not have full information. • She knew that she was the only person who knew how much each person received from the dictator. Participant Recipient Recipient Recipient Recipient Recipient 500 yen 500 yen 500 yen 500 yen 500 yen Dictator Since we used deception, actually all participants were chosen by lottery. 4500 yen By lottery one player was chosen as a person who could see the complete distribution of 7000 yen.

32. Privately knowing that everybody was treated unfairly is enough , and common knowledge is unnecessary Hypotheses There are 3 competing hypotheses regarding cooperation rate. H1: Only reduction of fear of greed occurs Participants would cooperate more in both Private and Common knowledge conditions than in Control condition. Hypothetical result Cooperation rate Control Private Common

33. Privately knowing that everybody was treated unfairly is not enough, and common knowledge is necessary Hypotheses There are 3 competing hypotheses regarding cooperation rate. H2: Only reduction of fear of fear occurs Participants would cooperate more in Common knowledge condition than in Control and Private knowledge conditions. Hypothetical result Cooperation rate Control Private Common

34. Both privately knowing that everybody was treated unfairly and common knowledge promote cooperation. Hypotheses There are 3 competing hypotheses regarding cooperation rate. H3: Both reduction of fear of greed and reduction of fear of fear occur. Cooperation rate would be lowest in Control condition and highest in Common knowledge condition. Hypothetical result Cooperation rate Control Private Common

35. Result (1) Cooperation rate Figure 1: Cooperation rate in each condition Dummy for Private knowledge condition: β = -0.11, n.s.Dummy for Common knowledge condition: β = 0.98, p<.05 Control Private Common Logistic regression DV: Cooperation=1, Defection =0 IV: Dummy for Private knowledge cond, Dummy for Common knowledge cond *Reference category – Control condition Participants cooperated more in Common knowledge condition than in the other two conditions. Hypothesis 2 was supported.

36. Participants cooperated more in Common knowledge condition because they expected more cooperation by the others. This result suggests that reduction of fear promoted cooperation Result (2) Effect of expectation The effect of common knowledge disappeared when we controlled expectation.

37. Conclusion Unfair treatment must be a common knowledge in order to induce a higher level of cooperation. This is because such a common knowledge reduces fear of fear rather than fear of greed. Summary and Conclusion Summary • Participants cooperated more in Common knowledge condition than in the other conditions. Participants cooperated more only when they knew that the other participants knew that everybody was treated unfairly.

38. Future directions Are there any factors other than the sense of unfairness that promote cooperation by reducing fear of fear through automatically activating the perception of common knowledge?

39. Thank you for your attention.

40. Hypotheses Cooperation rate (1) Participants would cooperate more in the unfair treatment conditions (private and common knowledge conditions) than in the control condition. The effect of unfair treatment by the dictator > Private knowledge condition Control condition Common knowledge condition (2) Participants would cooperate more in the common knowledge condition than in the private knowledge condition. The effect of common knowledge > Private knowledge condition Common knowledge condition

41. Result (1) Cooperation rate Figure 1: Cooperation rate in each condition Dummy for Private knowledge condition: β = -1.09, p<.05Dummy for Control condition: β = 0.98, p<.05 Logistic regression Dependent variable: Cooperation=0, Defection =1 Independent variable: Dummy for Private knowledge condition Dummy for Control condition Common knowledge condition – Reference category Participants cooperated more in Common knowledge condition than in the other two conditions. Hypothesis 2 was supported.

42. Experiment Control condition : Ordinary one-shot SD without any context • 5 players per group • Players first engaged in a social inference task (bogus task), and were paid 500 yen ($5) for completing the task. • Players were then asked if they want to provide 500 yen to the group. • If more than 3 players provided 500 yen to the group, everybody received 800 yen as a bonus. Cooperators receive 800 yen and defectors receive 1300 yen. • If less then 4 players provided 500 yen, then nobody received a bonus. Cooperators receive 0 yen and defectors receive 500 yen. We used deception: Although participants were told that there were other participants and that they would interact with them, actually each participant behaves as an individual. In other words, there was no real interaction with the other participants.

43. Experiment Control condition : Ordinary one-shot SD without any context • 2nd stage: One-shot step level SD Cooperation : Provide 500 yen to the groupDefection : Keep 500 yen for oneself 500 yen 500 yen 500 yen 500 yen 500 yen If more than 3 players cooperate, a public good (4000 yen) is provided. Total earnings of cooperators : 500-500+(4000/5)=800 yen defectors : 500-0+(4000/5)=1300 yen If less then 4 players cooperate, a public good is not provided.Total earnings of cooperators : 500-500=0 yen defectors : 500-0=500 yen

44. Experiment Common knowledge condition • 6 players per group • Players first engaged in a social inference task (bogus task), and were paid 7000 yen as a group. • A dictator was chosen randomly from the group and decided to allocate 7000 yen among group members. • The dictator allocated 4500 yen for himself and 500 yen for each of the other 5 players. • 5 players were then asked if they want to provide 500 yen. • If more than 3 players provided 500 yen to the group, 4000 yen was forfeited from the dictator and the other 5 players shared 4000 yen equally. In other words, each player received 800 yen. • If less then 4 players provided 500 yen, then nothing happens. Incentive structure is identical with the one in the other conditions. Successful restoration of fairness Unsuccessful restoration of fairness

45. Experiment Private knowledge condition • Identical with Common knowledge condition • The only difference is that participants are the only one who knew that everybody was treated unfairly by the dictator. After the dictator allocated 7000 yen, each player received an allocation sheet that says how much she was allocated by the dictator. Incentive structure is identical with the one in the other conditions. However, how much the other players’ received was not written on the allocation sheet. Then, by lottery one player was chosen as a person who could see the complete distribution of 7000 yen. Since we used deception, actually all participants were chosen by lottery.

46. Result (2) Effect of 2nd-order expectation What is your estimate of the other participants’ estimate of the probability that more than 3 participants provided the money? F（2,124）=6.66, p<.01 2nd-order expectation (expectation on expectation) was lower in Control condition than in the other 2 conditions.

47. Result (2) Effect of 2nd-order expectation The effect of common knowledge disappeared when we controlled 2nd-order expectation. Participants cooperated more in Common knowledge condition because they expected the other participants’ expectation of cooperation higher. Reduction of fear of fear plays a critical role.

48. Result (2) Effect of expectation What is your estimation of the probability that more than 3 participants provided the money? How many participants do you think have provided the money? F（2,124）=5.11, p<.01 F（2,123）=3.43, p<.05 Participants’ expectation was higher in Common knowledge condition than in Control condition.

49. Discussion • Participants cooperated more in Common knowledge condition than in the other conditions. Participants cooperated more only when they knew that the other participants knew that everybody was treated unfairly. Being treated unfairly makes people believe that it is a common knowledge. 2nd-order expectation plays a critical role