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Evolutionary Game Dynamics in Populations with Heterogenous Structures

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  • Wes Maciejewski
  • Feng Fu
  • Christoph Hauert

Abstract

Evolutionary graph theory is a well established framework for modelling the evolution of social behaviours in structured populations. An emerging consensus in this field is that graphs that exhibit heterogeneity in the number of connections between individuals are more conducive to the spread of cooperative behaviours. In this article we show that such a conclusion largely depends on the individual-level interactions that take place. In particular, averaging payoffs garnered through game interactions rather than accumulating the payoffs can altogether remove the cooperative advantage of heterogeneous graphs while such a difference does not affect the outcome on homogeneous structures. In addition, the rate at which game interactions occur can alter the evolutionary outcome. Less interactions allow heterogeneous graphs to support more cooperation than homogeneous graphs, while higher rates of interactions make homogeneous and heterogeneous graphs virtually indistinguishable in their ability to support cooperation. Most importantly, we show that common measures of evolutionary advantage used in homogeneous populations, such as a comparison of the fixation probability of a rare mutant to that of the resident type, are no longer valid in heterogeneous populations. Heterogeneity causes a bias in where mutations occur in the population which affects the mutant's fixation probability. We derive the appropriate measures for heterogeneous populations that account for this bias.Author Summary: Understanding the evolution of cooperation is a persistent challenge to evolutionary theorists. A contemporary take on this subject is to model populations with interactions structured as close as possible to actual social networks. These networks are heterogeneous in the number and type of contact each member has. Our paper demonstrates that the fate of cooperation in such heterogeneous populations critically depends on the rate at which interactions occur and how interactions translate into the fitnesses of the strategies. We also develop theory that allows for an evolutionary analysis in heterogeneous populations. This includes deriving appropriate criteria for evolutionary advantage.

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  • Wes Maciejewski & Feng Fu & Christoph Hauert, 2014. "Evolutionary Game Dynamics in Populations with Heterogenous Structures," PLOS Computational Biology, Public Library of Science, vol. 10(4), pages 1-16, April.
    • Handle: RePEc:plo:pcbi00:1003567
    DOI: 10.1371/journal.pcbi.1003567
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    1. Benjamin Allen & Christine Sample & Yulia Dementieva & Ruben C Medeiros & Christopher Paoletti & Martin A Nowak, 2015. "The Molecular Clock of Neutral Evolution Can Be Accelerated or Slowed by Asymmetric Spatial Structure," PLOS Computational Biology, Public Library of Science, vol. 11(2), pages 1-32, February.
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    4. Huang, Keke & Liu, Yishun & Zhang, Yichi & Yang, Chunhua & Wang, Zhen, 2018. "Understanding cooperative behavior of agents with heterogeneous perceptions in dynamic networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 234-240.
    5. Quan, Ji & Chen, Xinyue & Wang, Xianjia, 2024. "Repeated prisoner's dilemma games in multi-player structured populations with crosstalk," Applied Mathematics and Computation, Elsevier, vol. 473(C).
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    7. Sarkar, Bijan, 2021. "The cooperation–defection evolution on social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 584(C).
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    9. Alex McAvoy & Christoph Hauert, 2015. "Asymmetric Evolutionary Games," PLOS Computational Biology, Public Library of Science, vol. 11(8), pages 1-26, August.
    10. Boyu Zhang & Cong Li & Yi Tao, 2016. "Evolutionary Stability and the Evolution of Cooperation on Heterogeneous Graphs," Dynamic Games and Applications, Springer, vol. 6(4), pages 567-579, December.
    11. Sarkar, Bijan, 2018. "Moran-evolution of cooperation: From well-mixed to heterogeneous complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 319-334.
    12. Sakiyama, Tomoko, 2021. "A power law network in an evolutionary hawk–dove game," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    13. Li, Wen-Jing & Jiang, Luo-Luo & Chen, Zhi & Perc, Matjaž & Slavinec, Mitja, 2020. "Optimization of mobile individuals promotes cooperation in social dilemmas," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    14. Li, Xiaopeng & Hao, Gang & Zhang, Zhipeng & Xia, Chengyi, 2021. "Evolution of cooperation in heterogeneously stochastic interactions," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    15. Yao Meng & Sean P. Cornelius & Yang-Yu Liu & Aming Li, 2024. "Dynamics of collective cooperation under personalised strategy updates," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    16. Mark Broom & Jan Rychtář, 2018. "Ideal Cost-Free Distributions in Structured Populations for General Payoff Functions," Dynamic Games and Applications, Springer, vol. 8(1), pages 79-92, March.
    17. Sanz Nogales, Jose M. & Zazo, S., 2020. "Replicator based on imitation for finite and arbitrary networked communities," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    18. Deng, Zhenghong & Huang, Yijie & Gu, Zhiyang & Deng, Zhilong & Xu, Jiwei, 2018. "The evolution of cooperation in spatial multigame with voluntary participation," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 41-46.
    19. Huang, Keke & Chen, Xiaofang & Yu, Zhaofei & Yang, Chunhua & Gui, Weihua, 2018. "Heterogeneous cooperative belief for social dilemma in multi-agent system," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 572-579.
    20. Wang, Xianjia & Chen, Wenman, 2020. "Evolutionary dynamics in spatial threshold public goods game with the asymmetric return rate mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    21. Chu, Chen & Liu, Jinzhuo & Shen, Chen & Jin, Jiahua & Tang, Yunxuan & Shi, Lei, 2017. "Coevolution of game strategy and link weight promotes cooperation in structured population," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 28-32.

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