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Group size effects in social evolution

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  • Nöldeke, Georg
  • Peña, Jorge

Abstract

How the size of social groups affects the evolution of cooperative behaviors is a classic question in evolutionary biology. Here we investigate group size effects in evolutionary games in which individuals choose whether to cooperate or defect. We find that increasing the group size decreases the proportion of cooperators at both stable and unstable rest points of the replicator dynamics. This implies that larger group sizes can have negative effects (by reducing the amount of cooperation at stable polymorphisms) and positive effects (by enlarging the basin of attraction of more cooperative outcomes) on the evolution of cooperation. These two effects can be simultaneously present in games whose evolutionary dynamics features both stable and unstable rest points, such as public goods games with participation thresholds. Our theory recovers and generalizes previous results and is applicable to a broad variety of social interactions that have been studied in the literature.

Suggested Citation

  • Nöldeke, Georg & Peña, Jorge, 2018. "Group size effects in social evolution," IAST Working Papers 18-75, Institute for Advanced Study in Toulouse (IAST).
  • Handle: RePEc:tse:iastwp:32651
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    Cited by:

    1. Wang, Mengyao & Pan, Qiuhui & He, Mingfeng, 2020. "Individuals with the firm heart are conducive to cooperation in social dilemma," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    2. Nöldeke, Georg & Peña, Jorge, 2020. "Group size and collective action in a binary contribution game," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 42-51.
    3. Jann, Ole & Schottmüller, Christoph, 2021. "Regime change games with an active defender," Games and Economic Behavior, Elsevier, vol. 129(C), pages 96-113.
    4. 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.

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    More about this item

    Keywords

    evolution of cooperation; evolutionary game theory; replicator dynamics; public goods games;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods

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