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The Algebra of Assortative Encounters and the Evolution of Cooperation

  • Bergstrom, Ted

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.

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Paper provided by Department of Economics, UC Santa Barbara in its series University of California at Santa Barbara, Economics Working Paper Series with number qt8fm2t3nf.

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Date of creation: 25 Jul 2001
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Handle: RePEc:cdl:ucsbec:qt8fm2t3nf
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  1. Theodore C. Bergstrom, . "On the Evolution of Altruistic Ethical Rules for Siblings," ELSE working papers 017, ESRC Centre on Economics Learning and Social Evolution.
  2. Ted Bergstrom & Oded Stark, . "How Altruism Can Prevail in an Evolutionary Environment," Papers _024, University of Michigan, Department of Economics.
  3. Roger B. Myerson, 1990. "Viscous Population Equilibria," Discussion Papers 906, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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