The Algebra of Assortative Encounters and the Evolution of Cooperation

This paper explores the quantitative relation between non random, assortative matching and the maintenance of cooperative behavior under evolutionary dynamics. We consider a population of individuals who are \hardwired" to play either cooperate or defect. They meet other individuals according to some random process and play their programmed strategy in a game of Prisoners' Dilemma. The type that gets the higher expected payoff reproduces more rapidly. We de¯ne an index of assortativity of encounters and develop an \algebra of assortative encounters." In one set of applications, we calculate the index of assortativity for games between relatives with either cultural or genetic inheritance and we show the logical connection between the index of assortativity and Hamilton's theory of kin selection [5]. We also apply the index of assortativity to determine the population dynamics when players select their partners, using partially informative cues about each others' types