Towards Realistic Models for Evolution of Cooperation

1. Towards Realistic Models for Evolution of Cooperation LIK MUI

2. … about procedure … • Briefly go over the paper • Clarify major points • Describe simulations (not in paper)

3. RoadMap • Introduction • Cooperation Models • Simulations • Conclusion 

4. Evolution of Cooperation • Animals cooperate • Two questions: • How does cooperation as a strategy becomes stable evolutionarily? • How does cooperation arise in the first place?

5. Darwinian Natural Selection “Survival of the fittest” • If evolution is all about individual survival, how can cooperation be explained? • Fittest what?

6. Fittest what ? • Individual • Rational agency theory (Kreps, 1990) • Group • Group selection theory (Wilson, 1980) • Gene • Selfish gene hypothesis (Dawkins, 1979) • Organization • Classic organizational theory (Simon, 1969)

7. RoadMap • Introduction • Cooperation Models • Group Selection • Kinship Theory • Direct Reciprocity • Indirect Reciprocity • Social Learning • Simulations • Conclusion 

8. Group Selection • Intuition: we ban cannibalism but not carnivorousness • Population/species: basic unit of natural selection • Problem: explain war, family feud, competition, etc.

9. Kinship Theory I • Intuition: nepotism • Hamilton’s Rule: • Individuals show less aggression and more cooperation towards closer kin if rule is satisfied • Basis for most work on kinship theory • Wright’s Coefficient of Related: r • Self: r=1 • Siblings: r=0.5 • Grandparent-grandchild: r=0.25

10. Kinship Theory II • Cannot explain: • Competition in viscuous population • Symbioses • Dynamics of cooperation

11. Direct Reciprocity • Intuition: being nice to others who are nice • “Reciprocal Altruism” • Trivers (1971) • Tit-for-tat and PD tournament • Axelrod and Hamilton (1981) • Cannot explain: • We cooperate not only with people who cooperate with us

12. Indirect Reciprocity • Intuition: respect one who is famous • Social-biological justifications • Biology: generalized altruism (Trivers, 1971, 1985) • Sociobiology: Alexandar (1986) • Sociology: Ostrom (1998) • 3 types of indirect reciprocity: • Looped • Observer-based • Image-based

13. Indirect Reciprocity: Looped • Looped Indirect Reciprocity • Boyd and Richerson (1989)

14. Indirect Reciprocity: Observers • Observer-based Reciprocity • Pollock and Dugatkin (1992)

15. Indirect Reciprocity: Image • Image (reputation) based Reciprocity • Nowak and Sigmund (1998, 2000)

16. Social Learning • Intuition: imitate those who are successful • Cultural transmission • Boyd and Richerson (1982) • Docility • Simon (1990, 1991)

17. Critiques of Existing Models • Many theories each explaining one or a few aspects of cooperation • Unrealism of model assumptions

18. Unrealism for Existing Models • asexual, non-overlapping generations • simultaneous play for every interaction • c.f., Abell and Reyniers, 2000 • dyadic interactions • mostly predetermined behavior • c.f., May, 1987 (lack of modeling stochasticity) • discrete actions (cooperate or defect) • social structure and cooperation • c.f., Simon, 1991; Cohen, et al., 2001 • extend social learning • c.f., Simon, 1990

19. RoadMap • Introduction • Cooperation Models • Simulations • Nowak and Sigmund Game • Prisoner’s Dilemma Game • Simon’s Docility Hypothesis • Conclusion 

20. Nowak and Sigmund Game • Payoff Matrix C = 0.1 B = 1.0 • Image Adjustment A = 1

21. Using Global Image: 1 Run

22. Using Global Image: 100 Runs

23. Dynamics using Global Reputation

24. Using 10 Observers/Interactions

25. Evolutionary PD Game • Repeated Prisoners’ Dilemma Game • Agent Actions: Action = { cooperate, defect } • Payoff Matrix:

26. PD Game Agent Strategies • All defecting (AllD) • Tit-for-tat (TFT) • Reputational Tit-for-tat (RTFT): using various notions of reputation

27. Base Case: PD Game

28. Simple Groups: social structures • Group structure affects members • Interactions, observations, and knowledge • Persistent structure • Groups actions • Observed indirectly through member's actions

29. Group Membership • Member agents • Have public group identity • Directly associated with one environment • Group Structure is a Tree • Least common ancestral node (LCAN) • Events occur with respect to a shared environment

30. Shared Environment Example AgentsGroup A1,A2 G1 A3,A4 G2 A5,A2 G1 A1,A3 G0 A5,A3 G0

31. PD Game with Group Reputation(varying encounters per generation EPG)

32. PD Game with Group Reputation (100 EPG; varying Inter-group interaction probability)

33. Groups/Organizations: bounded rationality explanation • Docility • Cooperation (altruism) as an explanation for the formation of groups/organizations • Why individuals “identify” with a group? • boundedly rational individuals • increase their survival fitness (Simon, 1969, 1990, 1991)

34. PD Game with Docility(50 cooperators and 50 defectors; 100 EPG; 1.0 IP)

35. Conclusion • Reviewed 5 major approaches to study evolution of cooperation • Provided 2 main critiques for existing models • Constructed model extensions addressing the critiques

36. Implications for Computer Science • Artificial intelligence • Benevolent agents are not good enough (c.f., multi-agents systems) • Learning theory can be used to study evolution of cooperation • Systems • Improve system design by understanding the dynamics of agents • Accountability substrate needed for distributed systems

37. Future Plan • Extend the simple group social structure • Overlapping generations • Sexual reproduction • Extend social learning using realistic/robust learning model

38. Modeling Diploid Organisms

39. Modeling Diploid Organisms

40. Modeling Diploid Organisms One of 2 Child Chromosomes Parental Chromosomes

41. Simulation Demo • Recall PD payoff matrix: • PD strategies: viewed as a probability vectors • Strategy: <PI, PT, PR, PP, PS> • TFT: < 1, 1, 1, 0, 0 > • AllD: < 0, 0, 0, 0, 0 > • AllC: < 1, 1, 1, 1, 1 > • STFT: < 0, 1, 1, 0, 0 >

42. Simulation: a search problem • Search Optimal PD Strategy • Search space: I, T, R, P, S probabilities