The emergence of indirect reciprocity

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

2. 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 altruism exist in our society? • Kin selection (Hamilton, 1964) ←only among close kins. • Direct reciprocity (e. g., Tit for tat) ←only among two players. How can Indirect reciprocity emerge?

3. Two approaches • Theoretical approach How indirect reciprocity can emerge? • A series of computer simulation to find the strategy that makes indirect reciprocity possible • 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. Score • 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”. How to assign a score is regulated by a strategy. 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) .

5. 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 (2)The score of the recipient’s previous recipient (1) The recipient’s previous behavior gave Good or or Bad did not give current recipient current donor current recipient’s previous recipient

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 Table 1. Four genes that assign the score to others Current recipient’s previous recipient’s score

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.) Although every strategy gives to a good recipient, a pattern to assign a score is different in each strategy. Current recipient’s previous recipient’s score

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

10. Results (2)Strict discriminator Among 14 strategies, only GBBB (strict discriminator) could make indirect reciprocity possible. GBBB (strict discriminator) assigns good only to a recipient who gave to a good person. GBBB always dominates a population and maintains indirect reciprocity (20/20 replications, giving rate=0.81). Current recipient’s previous recipient’s score Current recipient’s previous behavior

11. Why could GBBB maintain indirect reciprocity? The key point to make indirect reciprocity possible is to drive out All-C which leads All-D to invade. ⇒GBBB doesn’t allow All-C to evolve. Current recipient’s previous recipient’s score 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).

12. Two approaches • Theoretical approach How indirect reciprocity can emerge? • A series of computer simulation to find the strategy that makes indirect reciprocity possible • 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. 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. 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. 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

15. A vignette study (2) • After reading each scenario, respondents answered their impressions about the target person who was described in the scenario. 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. Consistent with the conclusion of theoretical approach. (Saints who gave to a bad person should be driven out in situations of indirect reciprocity.) Results • Respondents evaluated • T1 (who gave to a good person) as “good” • T2 (who gave to a bad person) as “bad” • T3 (who didn’t give to a good person) as “bad” one of positive impression to the target

17. Consistent with the conclusion of theoretical approach. (Saints who gave to a bad person should be driven out in situations of indirect reciprocity.) Results • Respondents evaluated • T1 (who gave to a good person) as “good” • T2 (who gave to a bad person) as “bad” • T3 (who didn’t give to a good person) as “bad” one of positive impression to the target Next step: to examine whether people actuallyexclude such “saints” when they are in situation of indirect reciprocity? ← work in progress