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Statistics of the number of equilibria in random social dilemma evolutionary games with mutation

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  • Manh Hong Duong

    (University of Birmingham)

  • The Anh Han

    (Teesside University)

Abstract

In this paper, we study analytically the statistics of the number of equilibria in pairwise social dilemma evolutionary games with mutation where a game’s payoff entries are random variables. Using the replicator–mutator equations, we provide explicit formulas for the probability distributions of the number of equilibria as well as other statistical quantities. This analysis is highly relevant assuming that one might know the nature of a social dilemma game at hand (e.g., cooperation vs coordination vs anti-coordination), but measuring the exact values of its payoff entries is difficult. Our delicate analysis shows clearly the influence of the mutation probability on these probability distributions, providing insights into how varying this important factor impacts the overall behavioural or biological diversity of the underlying evolutionary systems. Graphic abstract

Suggested Citation

  • Manh Hong Duong & The Anh Han, 2021. "Statistics of the number of equilibria in random social dilemma evolutionary games with mutation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(8), pages 1-13, August.
    • Handle: RePEc:spr:eurphb:v:94:y:2021:i:8:d:10.1140_epjb_s10051-021-00181-0
    DOI: 10.1140/epjb/s10051-021-00181-0
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    References listed on IDEAS

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    1. Han, The Anh & Traulsen, Arne & Gokhale, Chaitanya S., 2012. "On equilibrium properties of evolutionary multi-player games with random payoff matrices," Theoretical Population Biology, Elsevier, vol. 81(4), pages 264-272.
    2. Manh Hong Duong & The Anh Han, 2020. "On Equilibrium Properties of the Replicator–Mutator Equation in Deterministic and Random Games," Dynamic Games and Applications, Springer, vol. 10(3), pages 641-663, September.
    3. Manh Hong Duong & The Anh Han, 2016. "On the Expected Number of Equilibria in a Multi-player Multi-strategy Evolutionary Game," Dynamic Games and Applications, Springer, vol. 6(3), pages 324-346, September.
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    Cited by:

    1. Zhang, Qinchunxue & Shu, Lan & Jiang, Bichuan, 2023. "Moran process in evolutionary game dynamics with interval payoffs and its application," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    2. Chen, Luoer & Deng, Churou & Duong, Manh Hong & Han, The Anh, 2024. "On the number of equilibria of the replicator-mutator dynamics for noisy social dilemmas," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).

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