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Asymmetric Evolutionary Games

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  • Alex McAvoy
  • Christoph Hauert

Abstract

Evolutionary game theory is a powerful framework for studying evolution in populations of interacting individuals. A common assumption in evolutionary game theory is that interactions are symmetric, which means that the players are distinguished by only their strategies. In nature, however, the microscopic interactions between players are nearly always asymmetric due to environmental effects, differing baseline characteristics, and other possible sources of heterogeneity. To model these phenomena, we introduce into evolutionary game theory two broad classes of asymmetric interactions: ecological and genotypic. Ecological asymmetry results from variation in the environments of the players, while genotypic asymmetry is a consequence of the players having differing baseline genotypes. We develop a theory of these forms of asymmetry for games in structured populations and use the classical social dilemmas, the Prisoner’s Dilemma and the Snowdrift Game, for illustrations. Interestingly, asymmetric games reveal essential differences between models of genetic evolution based on reproduction and models of cultural evolution based on imitation that are not apparent in symmetric games.Author Summary: Biological interactions, even between members of the same species, are almost always asymmetric due to differences in size, access to resources, or past interactions. However, classical game-theoretical models of evolution fail to account for sources of asymmetry in a comprehensive manner. Here, we extend the theory of evolutionary games to two general classes of asymmetry arising from environmental variation and individual differences, covering much of the heterogeneity observed in nature. If selection is weak, evolutionary processes based on asymmetric interactions behave macroscopically like symmetric games with payoffs that may depend on the resource distribution in the population or its structure. Asymmetry uncovers differences between genetic and cultural evolution that are not apparent when interactions are symmetric.

Suggested Citation

  • Alex McAvoy & Christoph Hauert, 2015. "Asymmetric Evolutionary Games," PLOS Computational Biology, Public Library of Science, vol. 11(8), pages 1-26, August.
    • Handle: RePEc:plo:pcbi00:1004349
    DOI: 10.1371/journal.pcbi.1004349
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    References listed on IDEAS

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    Cited by:

    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. Meng Ding & Hui Zeng, 2022. "Multi-Agent Evolutionary Game in the Recycling Utilization of Sulfate-Rich Wastewater," IJERPH, MDPI, vol. 19(14), pages 1-20, July.
    3. Liu, Yuan & Cao, Lixuan & Wu, Bin, 2022. "General non-linear imitation leads to limit cycles in eco-evolutionary dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    4. Han, Jia-Xu & Wang, Rui-Wu, 2023. "Complex interactions promote the frequency of cooperation in snowdrift game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    5. Michael Foley & Rory Smead & Patrick Forber & Christoph Riedl, 2021. "Avoiding the bullies: The resilience of cooperation among unequals," PLOS Computational Biology, Public Library of Science, vol. 17(4), pages 1-18, April.
    6. Liu, Yandi & Wang, Hexin & Ding, Yi & Yang, Xuan & Dai, Yu, 2022. "Can weak diversity help in propagating cooperation? Invasion of cooperators at the conformity-conflict boundary," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    7. Qi Su & Lei Zhou & Long Wang, 2019. "Evolutionary multiplayer games on graphs with edge diversity," PLOS Computational Biology, Public Library of Science, vol. 15(4), pages 1-22, April.
    8. Zhang, Zhipeng & Wu, Yu’e & Zhang, Shuhua, 2022. "Reputation-based asymmetric comparison of fitness promotes cooperation on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P1).
    9. Liu, Xuesong & Pan, Qiuhui & He, Mingfeng & Liu, Aizhi, 2019. "Promotion of cooperation in evolutionary game dynamics under asymmetric information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 258-266.
    10. Marta C. Couto & Saptarshi Pal, 2023. "Introspection Dynamics in Asymmetric Multiplayer Games," Dynamic Games and Applications, Springer, vol. 13(4), pages 1256-1285, December.
    11. Liu, Yifan & Geng, Yini & Du, Chunpeng & Hu, Kaipeng & Shen, Chen & Pansini, Riccardo & Shi, Lei, 2021. "The interface of unidirectional rewards: Enhanced cooperation within interdependent networks," Applied Mathematics and Computation, Elsevier, vol. 402(C).

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