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The Algebra of Assortative Encounters and the Evolution of Cooperation

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Author Info
Ted Bergstrom (University of California, Santa Barbara)

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Abstract

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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File URL: http://repositories.cdlib.org/cgi/viewcontent.cgi?article=1042&context=ucsbecon
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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 wp13-01.

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Date of creation: 25 Jul 2001
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Handle: RePEc:cdl:ucsbec:wp13-01

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Keywords: Algebra ; Assortative ; Encounters; Evolution ; Cooperation ;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Ted Bergstrom, 1995. "On the Evolution of Altruistic Ethical Rules for Siblings," University of California at Santa Barbara, Economics Working Paper Series 1995A, Department of Economics, UC Santa Barbara. [Downloadable!]
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  2. Myerson, Roger B. & Pollock, Gregory B. & Swinkels, Jeroen M., 1991. "Viscous population equilibria," Games and Economic Behavior, Elsevier, vol. 3(1), pages 101-109, February. [Downloadable!] (restricted)
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  3. Ted Bergstrom & Oded Stark, 1993. "How Altruism Can Prevail in an Evolutionary Environment," University of California at Santa Barbara, Economics Working Paper Series 1993B, Department of Economics, UC Santa Barbara. [Downloadable!]
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  4. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, December.
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Alger, Ingela & Weibull, Jörgen, 2007. "The Fetters of the Sib: Weber Meets Darwin," Working Paper Series in Economics and Finance 682, Stockholm School of Economics. [Downloadable!]
    Other versions:
  2. Ted Bergstrom, 2001. "Evolution of Social Behavior: Individual and Group Selection Models," University of California at Santa Barbara, Economics Working Paper Series wp14-01, Department of Economics, UC Santa Barbara. [Downloadable!]
    Other versions:
  3. Thierry Vignolo, 2007. "Imitation and Selective Matching in Reputational Games," Economics Working Papers ECO2007/31, European University Institute. [Downloadable!]
  4. Chun-Lei Yang & Ching-Syang Jack Yue & I-Tang Yu, 2007. "The rise of cooperation in correlated matching prisoners dilemma: An experiment," Experimental Economics, Springer, vol. 10(1), pages 3-20, March. [Downloadable!] (restricted)
  5. Deby Cassill & Indira Kuriachan & S. Vinson, 2007. "A Test of Two Skew Models to Explain Cooperative Breeding," Journal of Bioeconomics, Springer, vol. 9(1), pages 19-37, April. [Downloadable!] (restricted)
  6. Ingela Alger & Jörgen W. Weibull, 2006. "Altruism and Climate," Boston College Working Papers in Economics 643, Boston College Department of Economics. [Downloadable!]
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  7. Philipp C. Wichardt, 2007. "Why and How Identity Should Influence Utility," Discussion Papers 193, SFB/TR 15 Governance and the Efficiency of Economic Systems, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich. [Downloadable!]
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