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General conditions for strategy abundance through a self-referential mechanism under weak selection

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  • Sekiguchi, Takuya

Abstract

We examine stochastic evolutionary game dynamics of two-player m×m symmetric and m×n asymmetric games in finite populations assuming that a player decides to change her current strategy on the basis of her dissatisfaction, which we call a self-referential mechanism. We derive the general expression for the stationary distribution of strategy under weak selection and compare it with the counterpart of a Moran process. As a result, we find that both in symmetric games and in asymmetric games, the self-referential mechanism always generates a greater gap between the favored and unfavored strategies’ frequencies for a fixed parameter set than does a Moran process. Further, we found that for small mutation rates, our results are almost identical to the counterpart of a Moran process.

Suggested Citation

  • Sekiguchi, Takuya, 2013. "General conditions for strategy abundance through a self-referential mechanism under weak selection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(13), pages 2886-2892.
  • Handle: RePEc:eee:phsmap:v:392:y:2013:i:13:p:2886-2892
    DOI: 10.1016/j.physa.2013.03.004
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    Cited by:

    1. Takuya Sekiguchi & Hisashi Ohtsuki, 2017. "Fixation Probabilities of Strategies for Bimatrix Games in Finite Populations," Dynamic Games and Applications, Springer, vol. 7(1), pages 93-111, March.
    2. Takuya Sekiguchi, 2023. "Fixation Probabilities of Strategies for Trimatrix Games and Their Applications to Triadic Conflict," Dynamic Games and Applications, Springer, vol. 13(3), pages 1005-1033, September.
    3. Sekiguchi, Takuya, 2023. "Abundance of strategies for trimatrix games in finite populations," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    4. Quan, Ji & Liu, Wei & Chu, Yuqing & Wang, Xianjia, 2018. "Stochastic dynamics and stable equilibrium of evolutionary optional public goods game in finite populations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 123-134.
    5. Marta C. Couto & Saptarshi Pal, 2023. "Introspection Dynamics in Asymmetric Multiplayer Games," Dynamic Games and Applications, Springer, vol. 13(4), pages 1256-1285, December.

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