1. 1 The emergence of indirect reciprocity Rie Mashima Nobuyuki Takahashi Theoretical and empirical approaches toward indirect reciprocity

2. 2 1)Kin selection (Hamilton, 1964) ←only among close kins. 2)Direct reciprocity ( e. g., Tit for tat) ←only among two players. ◆ How can altruism exist in our society? 3)Indirect reciprocity (generalized exchange) Indirect reciprocity can make altruism possible among N- person. When a person who helps the other person is reciprocated not by the helped person but by another person. How can Indirect reciprocity emerge?

3. 3 Two approaches 1.Theoretical approach How indirect reciprocity can emerge? –A series of computer simulation to find the strategy that makes indirect reciprocity possible 2.Empirical approach  A vignette study to examine what type of person people actually regard as “Good” (i.e., worth giving to), and as “Bad” (i.e., not worth giving to) in the situation of indirect reciprocity.

4. 4 Framework of giving game A pair of donor and recipient is randomly chosen. A donor decides whether to give his resource to his recipient with a cost of c (recipient receives the benefit b :b>c). Each player has a reputation score which has two values: “good” or “bad”. A donor gives if he thinks the recipient’s score is “good”. A donor doesn’t give if he thinks the recipient’s score is “bad”. Score How to assign a score is regulated by a strategy.

5. 5 Strategy current donor current recipient A donor assigns a score to a recipient by using two types of information. (1)The recipient’s previous behavior (2)The score of the recipient’s previous recipient did not give gave or (1) The recipient’s previous behavior current recipient’s previous recipient (2)The score of the recipient’s previous recipient Good or Bad

6. 6 Strategy A donor assigns a score to a recipient by using two types of information. (1)The recipient’s previous behavior (2)The score of the recipient’s previous recipient Current recipient’s previous behavior GoodBad Gave ① Good or Bad ② Good or Bad Did not give ③ Good or Bad ④ Good or Bad Table 1. Four genes that assign the score to others Current recipient’s previous recipient’s score

7. 7 Strategy ・ 4 genes determine how to assign a score to each type of others by using two types of information. ・ Strategies are represented by the sets of 4 genes. (e. g. GGGG→All-C (unconditional cooperator) BBBB→All-D (unconditional defector) … 16 strategies are possible.) Current recipient’s previous behavior GoodBad Gave ① Good or Bad ② Good or Bad Did not give ③ Good or Bad ④ Good or Bad Current recipient’s previous recipient’s score Although every strategy gives to a good recipient, a pattern to assign a score is different in each strategy.

8. 8 What kind of strategy is solution? Evolutionary computer simulation There are 3 strategies: All-C, All-D, and one of the 14 strategies. (14 strategies consist of all possible strategies except for All-C(GGGG), All-D(BBBB)) On each round a pair of donor and recipient is chosen randomly, and plays a giving game. 1500 rounds per generation (m=1500) At the end of each generation, Selection and Mutation occur (mutation rate:μ=0.0001). Size of group (n)=300, έ = 0.025, δ=0.025, b/c ratio = 2, 4, 6, 8, 10.

9. 9 Results (1) GGBB: Image scoring strategy (Nowak & Sigmund, 1998) GoodBad Gave Good Did not giveBad GGBG: Standing strategy (L & H, 2001; P & B, 2003) GoodBad Gave Good Did not giveBadGood All-D dominated in 20/20 replications. All-D dominated in 6/20 replications. Strategies provided by previous studies …Only one strategy could make indirect reciprocity emerge. All strategies which were provided by previous studies cannot make indirect reciprocity possible. × ×

10. 10 GBBB (strict discriminator) assigns good only to a recipient who gave to a good person. Results (2) Strict discriminator Among 14 strategies, only GBBB (strict discriminator) could make indirect reciprocity possible. Current recipient’s previous recipient’s score GoodBad Gave Good Bad Did not giveBad Current recipient’s previous behavior GBBB always dominates a population and maintains indirect reciprocity (20/20 replications, giving rate=0.81).

11. 11 Why could GBBB maintain indirect reciprocity? ⇒ GBBB doesn’t allow All-C to evolve. Current recipient’s previous recipient’s score GoodBad Gave Good Bad Did not giveBad Current recipient’s previous behavior Being different from other discriminative strategies, GBBB does not allow a person who gave to a bad person to evolve. ⇒ GBBB does not allow All-C to evolve ⇒ GBBB can prevent All-D from invading (because increase of All-C leads invasion of All-D). The key point to make indirect reciprocity possible is to drive out All-C which leads All-D to invade.

12. 12 Two approaches 1.Theoretical approach How indirect reciprocity can emerge? A series of computer simulation to find the strategy that makes indirect reciprocity possible 2.Empirical approach  Do people adopt strategies which exclude unconditional cooperators?  A vignette study to examine what type of person people actually regard as “Good” (i.e., worth giving to), and as “Bad” (i.e., not worth giving to) in the situation of indirect reciprocity.

13. 13 A vignette study (1) All respondents read four scenarios of situations of indirect reciprocity. Each scenario described what the target person (T1 - T4) did to potential recipients.

14. 14 A vignette study (1) All respondents read four scenarios of situations of indirect reciprocity. Each scenario described what the target person (T1 - T4) did to potential recipients. GoodBad GaveT1: GtoGT2: GtoB Did not giveT3: NGtoGT4: NGtoB T1: a person who gave to a good person T2: a person who gave to a bad person T3: a person who did not give to a good person T4: a person who did not give to a bad person Four types of target person

15. 15 A vignette study (2) After reading each scenario, respondents answered their impressions about the target person who was described in the scenario. GoodBad GaveT1: GtoGT2: GtoB Did not giveT3: NGtoGT4: NGtoB Four types of target person T1: a person who gave to a good person T2: a person who gave to a bad person T3: a person who did not give to a good person T4: a person who did not give to a bad person

16. 16 Results Respondents evaluated 1.T1 (who gave to a good person) as “good” 2.T2 (who gave to a bad person) as “bad” 3.T3 (who didn’t give to a good person) as “bad” GoodBad GaveT1: GtoGT2: GtoB Did not giveT3: NGtoGT4: NGtoB Consistent with the conclusion of theoretical approach. (Saints who gave to a bad person should be driven out in situations of indirect reciprocity.) one of positive impression to the target

17. 17 Results Respondents evaluated 1.T1 (who gave to a good person) as “good” 2.T2 (who gave to a bad person) as “bad” 3.T3 (who didn’t give to a good person) as “bad” GoodBad GaveT1: GtoGT2: GtoB Did not giveT3: NGtoGT4: NGtoB Consistent with the conclusion of theoretical approach. (Saints who gave to a bad person should be driven out in situations of indirect reciprocity.) one of positive impression to the target Next step: to examine whether people actually exclude such “saints” when they are in situation of indirect reciprocity? ← work in progress