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Stochastic stability analysis of evolutionary two-player games on regular graphs

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  • Zhou, Zhao
  • Liang, Haili
  • Su, Housheng
  • Xu, Xinjian
  • Du, Wenli

Abstract

We study evolutionary two-player games and identify stochastically stable equilibria of the network games restricted to infinite populations on regular graphs. The players update their strategies according to four different rules: birth–death, death–birth, imitation and pairwise comparison for prisoner’s dilemma and snowdrift games, respectively. For two-player games on regular graphs, we show that there is a unique stochastically stable equilibrium for infinite populations. For the prisoner’s dilemma game, if the benefit-to-cost ratio is larger than k+2 (k is the degree of a regular graph), the networked game has a higher fraction of cooperators than that for a well-mixed population. For the snowdrift game, the fraction of cooperators in a regular graph would be higher than that of the well-mixed population, if the benefit-to-cost ratio is larger than 1.5. Under certain conditions, the lower graph connectivity can lead to the emergence of more cooperators. Finally, some numerical simulation examples are given to demonstrate the theoretical results.

Suggested Citation

  • Zhou, Zhao & Liang, Haili & Su, Housheng & Xu, Xinjian & Du, Wenli, 2019. "Stochastic stability analysis of evolutionary two-player games on regular graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    • Handle: RePEc:eee:phsmap:v:535:y:2019:i:c:s0378437119313615
    DOI: 10.1016/j.physa.2019.122364
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    References listed on IDEAS

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    1. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    2. Hisashi Ohtsuki & Christoph Hauert & Erez Lieberman & Martin A. Nowak, 2006. "A simple rule for the evolution of cooperation on graphs and social networks," Nature, Nature, vol. 441(7092), pages 502-505, May.
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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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