Towards Realistic Models for Evolution of Cooperation LIK MUI

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

RoadMap  Introduction Cooperation Models Simulations Conclusion

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

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

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

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

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

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

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

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

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

Indirect Reciprocity: Looped Looped Indirect Reciprocity Boyd and Richerson (1989)

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

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

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

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

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

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

Nowak and Sigmund Game Payoff Matrix Image Adjustment Interact B = 1.0 Image Adjustment A = 1 Interact Not interact Donor -C Recipient B Interact Not interact Donor A -A Recipient

Using Global Image: 1 Run

Using Global Image: 100 Runs

Dynamics using Global Reputation

Using 10 Observers/Interactions

Action = { cooperate, defect } Evolutionary PD Game Repeated Prisoners’ Dilemma Game Agent Actions: Action = { cooperate, defect } Payoff Matrix: C D 3/3 0/5 5/0 1/1

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

Base Case: PD Game

Simple Groups: social structures Group structure affects members Interactions, observations, and knowledge Persistent structure Groups actions Observed indirectly through member's actions Hierarchy family, school, town, country Structure member identity, isolation (different islands) integration (shared habitat) groups could evolve

Group Membership Member agents Group Structure is a Tree 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 Events occur in shared environment simple analogy to human society strangers often attempt to find shared reference point in initial conversation

Shared Environment Example Agents Group A1,A2 G1 A3,A4 G2 A5,A2 G1 A1,A3 G0 A5,A3 G0 People belong to different families People interact as members of shared community town, religious group, school

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

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

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)

PD Game with Docility (50 cooperators and 50 defectors; 100 EPG; 1 PD Game with Docility (50 cooperators and 50 defectors; 100 EPG; 1.0 IP)

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

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

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

Modeling Diploid Organisms

Modeling Diploid Organisms

Modeling Diploid Organisms Parental Chromosomes One of 2 Child Chromosomes

Simulation Demo C D R/R S/T T/S P/P 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 >

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