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The Algebra of Assortative Encounters and the Evolution of Cooperation

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  • Bergstrom, Ted

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.

Suggested Citation

  • Bergstrom, Ted, 2001. "The Algebra of Assortative Encounters and the Evolution of Cooperation," University of California at Santa Barbara, Economics Working Paper Series qt8fm2t3nf, Department of Economics, UC Santa Barbara.
  • Handle: RePEc:cdl:ucsbec:qt8fm2t3nf
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    References listed on IDEAS

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    1. Bergstrom, Theodore C, 1995. "On the Evolution of Altruistic Ethical Rules for Siblings," American Economic Review, American Economic Association, vol. 85(1), pages 58-81, March.
    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.
    3. Bergstrom, Theodore C & Stark, Oded, 1993. "How Altruism Can Prevail in an Evolutionary Environment," American Economic Review, American Economic Association, vol. 83(2), pages 149-155, May.
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    Citations

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    Cited by:

    1. 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.
    2. Ingela Alger & Jörgen W. Weibull, 2013. "Homo Moralis—Preference Evolution Under Incomplete Information and Assortative Matching," Econometrica, Econometric Society, vol. 81(6), pages 2269-2302, November.
    3. Alger, Ingela & Lehmann, Laurent & Weibull, Jörgen W., 2018. "Uninvadable social behaviors and preferences in group-structured populations," TSE Working Papers 18-888, Toulouse School of Economics (TSE).
    4. Ingela Alger, 2010. "Public Goods Games, Altruism, and Evolution," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 12(4), pages 789-813, August.
    5. repec:eee:gamebe:v:106:y:2017:i:c:p:260-276 is not listed on IDEAS
    6. Ingela Alger & Jörgen W. Weibull, 2010. "Kinship, Incentives, and Evolution," American Economic Review, American Economic Association, vol. 100(4), pages 1725-1758, September.
    7. Ingela Alger & Jörgen W. Weibull, 2010. "Evolutionary Stability, Co-operation and Hamilton’s Rule," Carleton Economic Papers 10-11, Carleton University, Department of Economics, revised 18 Jan 2011.
    8. repec:eee:ecolet:v:163:y:2018:i:c:p:146-148 is not listed on IDEAS
    9. Qu, Xinglong & Zhou, Changli & Cao, Zhigang & Yang, Xiaoguang, 2016. "Conditional dissociation as a punishment mechanism in the evolution of cooperation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 449(C), pages 215-223.
    10. repec:wsi:igtrxx:v:19:y:2017:i:04:n:s0219198917500190 is not listed on IDEAS
    11. Florian Herold, 2012. "Carrot or Stick? The Evolution of Reciprocal Preferences in a Haystack Model," American Economic Review, American Economic Association, vol. 102(2), pages 914-940, April.
    12. Bergstrom, Ted, 2001. "Evolution of Social Behavior: Individual and Group Selection Models," University of California at Santa Barbara, Economics Working Paper Series qt2bh2x16r, Department of Economics, UC Santa Barbara.
    13. repec:eee:eecrev:v:102:y:2018:i:c:p:1-18 is not listed on IDEAS

    More about this item

    Keywords

    Algebra; Assortative; Encounters; Evolution; Cooperation;

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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