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Dynamic Properties of Evolutionary Multi-player Games in Finite Populations

Author

Listed:
  • Bin Wu

    (Evolutionary Theory Group, Max-Planck-Institute for Evolutionary Biology, August-Thienemann-Straße 2, 24306 Plön, Germany)

  • Arne Traulsen

    (Evolutionary Theory Group, Max-Planck-Institute for Evolutionary Biology, August-Thienemann-Straße 2, 24306 Plön, Germany)

  • Chaitanya S. Gokhale

    (Evolutionary Theory Group, Max-Planck-Institute for Evolutionary Biology, August-Thienemann-Straße 2, 24306 Plön, Germany)

Abstract

William D. Hamilton famously stated that “human life is a many person game and not just a disjoined collection of two person games”. However, most of the theoretical results in evolutionary game theory have been developed for two player games. In spite of a multitude of examples ranging from humans to bacteria, multi-player games have received less attention than pairwise games due to their inherent complexity. Such complexities arise from the fact that group interactions cannot always be considered as a sum of multiple pairwise interactions. Mathematically, multi-player games provide a natural way to introduce non-linear, polynomial fitness functions into evolutionary game theory, whereas pairwise games lead to linear fitness functions. Similarly, studying finite populations is a natural way of introducing intrinsic stochasticity into population dynamics. While these topics have been dealt with individually, few have addressed the combination of finite populations and multi-player games so far. We are investigating the dynamical properties of evolutionary multi-player games in finite populations. Properties of the fixation probability and fixation time, which are relevant for rare mutations, are addressed in well mixed populations. For more frequent mutations, the average abundance is investigated in well mixed as well as in structured populations. While the fixation properties are generalizations of the results from two player scenarios, addressing the average abundance in multi-player games gives rise to novel outcomes not possible in pairwise games.

Suggested Citation

  • Bin Wu & Arne Traulsen & Chaitanya S. Gokhale, 2013. "Dynamic Properties of Evolutionary Multi-player Games in Finite Populations," Games, MDPI, vol. 4(2), pages 1-18, May.
  • Handle: RePEc:gam:jgames:v:4:y:2013:i:2:p:182-199:d:25483
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Du, Faqi & Fu, Feng, 2013. "Quantifying the impact of noise on macroscopic organization of cooperation in spatial games," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 35-44.
    2. Bin Wu & Julián García & Christoph Hauert & Arne Traulsen, 2013. "Extrapolating Weak Selection in Evolutionary Games," PLOS Computational Biology, Public Library of Science, vol. 9(12), pages 1-7, December.
    3. Bin Wu & Lei Zhou, 2018. "Individualised aspiration dynamics: Calculation by proofs," PLOS Computational Biology, Public Library of Science, vol. 14(9), pages 1-15, September.
    4. Xia, Ke, 2021. "Average abundance function of multi-player threshold public goods without initial endowment evolutionary game model under differential aspiration levels and redistribution mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    5. Gu, Cuiling & Wang, Xianjia & Ding, Rui & Zhao, Jinhua & Liu, Yang, 2022. "Evolutionary dynamics of multi-player snowdrift games based on the Wright-Fisher process," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    6. D. Timothy Bishop & Mark Broom & Richard Southwell, 2020. "Chris Cannings: A Life in Games," Dynamic Games and Applications, Springer, vol. 10(3), pages 591-617, September.
    7. Chaitanya S. Gokhale & Joseph Bulbulia & Marcus Frean, 2022. "Collective narratives catalyse cooperation," Palgrave Communications, Palgrave Macmillan, vol. 9(1), pages 1-9, December.
    8. 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.
    9. Xia, Ke, 2021. "The characteristics of average abundance function of multi-player threshold public goods evolutionary game model under redistribution mechanism," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    10. McCandlish, David M. & Epstein, Charles L. & Plotkin, Joshua B., 2015. "Formal properties of the probability of fixation: Identities, inequalities and approximations," Theoretical Population Biology, Elsevier, vol. 99(C), pages 98-113.
    11. Marta C. Couto & Saptarshi Pal, 2023. "Introspection Dynamics in Asymmetric Multiplayer Games," Dynamic Games and Applications, Springer, vol. 13(4), pages 1256-1285, December.
    12. 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.
    13. Éloi Martin & Sabin Lessard, 2023. "Assortment by Group Founders Always Promotes the Evolution of Cooperation Under Global Selection But Can Oppose it Under Local Selection," Dynamic Games and Applications, Springer, vol. 13(4), pages 1194-1218, December.
    14. Zhang, Wei & Brandes, Ulrik, 2023. "Is cooperation sustained under increased mixing in evolutionary public goods games on networks?," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    15. Dhaker Kroumi & Éloi Martin & Cong Li & Sabin Lessard, 2021. "Effect of Variability in Payoffs on Conditions for the Evolution of Cooperation in a Small Population," Dynamic Games and Applications, Springer, vol. 11(4), pages 803-834, December.
    16. Jorge Peña & Bin Wu & Jordi Arranz & Arne Traulsen, 2016. "Evolutionary Games of Multiplayer Cooperation on Graphs," PLOS Computational Biology, Public Library of Science, vol. 12(8), pages 1-15, August.

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