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Evolution of social behavior in finite populations: A payoff transformation in general n-player games and its implications

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  • Kurokawa, Shun
  • Ihara, Yasuo

Abstract

The evolution of social behavior has been the focus of many theoretical investigations, which typically have assumed infinite populations and specific payoff structures. This paper explores the evolution of social behavior in a finite population using a general n-player game. First, we classify social behaviors in a group of n individuals based on their effects on the actor’s and the social partner’s payoffs, showing that in general such classification is possible only for a given composition of strategies in the group. Second, we introduce a novel transformation of payoffs in the general n-player game to formulate explicitly the effects of a social behavior on the actor’s and the social partners’ payoffs. Third, using the transformed payoffs, we derive the conditions for a social behavior to be favored by natural selection in a well-mixed population and in the presence of multilevel selection.

Suggested Citation

  • Kurokawa, Shun & Ihara, Yasuo, 2013. "Evolution of social behavior in finite populations: A payoff transformation in general n-player games and its implications," Theoretical Population Biology, Elsevier, vol. 84(C), pages 1-8.
    • Handle: RePEc:eee:thpobi:v:84:y:2013:i:c:p:1-8
    DOI: 10.1016/j.tpb.2012.11.004
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    References listed on IDEAS

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    1. Kurokawa, Shun & Wakano, Joe Yuichiro & Ihara, Yasuo, 2010. "Generous cooperators can outperform non-generous cooperators when replacing a population of defectors," Theoretical Population Biology, Elsevier, vol. 77(4), pages 257-262.
    2. Julián García & Arne Traulsen, 2012. "The Structure of Mutations and the Evolution of Cooperation," PLOS ONE, Public Library of Science, vol. 7(4), pages 1-9, April.
    3. Martin A. Nowak & Akira Sasaki & Christine Taylor & Drew Fudenberg, 2004. "Emergence of cooperation and evolutionary stability in finite populations," Nature, Nature, vol. 428(6983), pages 646-650, April.
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    Cited by:

    1. Chaitanya Gokhale & Arne Traulsen, 2014. "Evolutionary Multiplayer Games," Dynamic Games and Applications, Springer, vol. 4(4), pages 468-488, December.
    2. Kurokawa, Shun, 2022. "Evolution of trustfulness in the case where resources for cooperation are sometimes absent," Theoretical Population Biology, Elsevier, vol. 145(C), pages 63-79.
    3. Fukutomi, Masao & Kurokawa, Shun, 2018. "How much cost should reciprocators pay in order to distinguish the opponent's cooperation from the opponent's defection?," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 301-314.
    4. Kurokawa, Shun, 2024. "Evolution of spite versus evolution of altruism through a disbandment mechanism," Theoretical Population Biology, Elsevier, vol. 156(C), pages 131-147.
    5. Shun Kurokawa & Joe Yuichiro Wakano & Yasuo Ihara, 2018. "Evolution of Groupwise Cooperation: Generosity, Paradoxical Behavior, and Non-Linear Payoff Functions," Games, MDPI, vol. 9(4), pages 1-24, December.
    6. Van Cleve, Jeremy & Lehmann, Laurent, 2013. "Stochastic stability and the evolution of coordination in spatially structured populations," Theoretical Population Biology, Elsevier, vol. 89(C), pages 75-87.
    7. Kurokawa, Shun, 2019. "How memory cost, switching cost, and payoff non-linearity affect the evolution of persistence," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 174-192.
    8. Bin Wu & Arne Traulsen & Chaitanya S. Gokhale, 2013. "Dynamic Properties of Evolutionary Multi-player Games in Finite Populations," Games, MDPI, vol. 4(2), pages 1-18, May.

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