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Abundance of strategies for trimatrix games in finite populations

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  • Sekiguchi, Takuya

Abstract

In this study, we aim to capture the consequences of stochastic evolutionary dynamics of trimatrix games in finite populations from the viewpoint of strategy abundances characterized by the stationary distribution of strategy frequencies. We then apply the obtained general result to some specific games that are important to consider the three-person social relationships. We investigate which set of strategies is most likely to be observed in evolutionary dynamics. Furthermore, we compare between the results of this study and those of previous studies relying on the concepts of ‘subgame perfection’ and ‘fixation probability.’ As a result, we find that sets of strategies, which are not supported by either of those previous studies, can be most frequently observed in our dynamics. Besides, the implication of the present result for the establishment of cooperative relationships is also discussed.

Suggested Citation

  • Sekiguchi, Takuya, 2023. "Abundance of strategies for trimatrix games in finite populations," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    • Handle: RePEc:eee:apmaco:v:448:y:2023:i:c:s009630032300111x
    DOI: 10.1016/j.amc.2023.127942
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    1. Veller, Carl & Hayward, Laura K., 2016. "Finite-population evolution with rare mutations in asymmetric games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 93-113.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
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