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Evolution of cooperation with respect to fixation probabilities in multi-player games with random payoffs

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  • Kroumi, Dhaker
  • Martin, Éloi
  • Lessard, Sabin

Abstract

We study the effect of variability in payoffs on the evolution of cooperation (C) against defection (D) in multi-player games in a finite well-mixed population. We show that an increase in the covariance between any two payoffs to D, or a decrease in the covariance between any two payoffs to C, increases the probability of ultimate fixation of C when represented once, and decreases the corresponding fixation probability for D. This is also the case with an increase in the covariance between any payoff to C and any payoff to D if and only if the sum of the numbers of C-players in the group associated with these payoffs is large enough compared to the group size. In classical social dilemmas with random cost and benefit for cooperation, the evolution of C is more likely to occur if the variances of the cost and benefit, as well as the group size, are small, while the covariance between cost and benefit is large.

Suggested Citation

  • Kroumi, Dhaker & Martin, Éloi & Lessard, Sabin, 2022. "Evolution of cooperation with respect to fixation probabilities in multi-player games with random payoffs," Theoretical Population Biology, Elsevier, vol. 145(C), pages 1-21.
    • Handle: RePEc:eee:thpobi:v:145:y:2022:i:c:p:1-21
    DOI: 10.1016/j.tpb.2022.02.001
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    References listed on IDEAS

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    1. Li, Cong & Lessard, Sabin, 2020. "Randomized matrix games in a finite population: Effect of stochastic fluctuations in the payoffs on the evolution of cooperation," Theoretical Population Biology, Elsevier, vol. 134(C), pages 77-91.
    2. Fudenberg, D. & Harris, C., 1992. "Evolutionary dynamics with aggregate shocks," Journal of Economic Theory, Elsevier, vol. 57(2), pages 420-441, August.
    3. Kroumi, Dhaker & Lessard, Sabin, 2015. "Evolution of cooperation in a multidimensional phenotype space," Theoretical Population Biology, Elsevier, vol. 102(C), pages 60-75.
    4. 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.
    5. Martin A. Nowak & Akira Sasaki & Christine Taylor & Drew Fudenberg, 2004. "Emergence of cooperation and evolutionary stability in finite populations," Nature, Nature, vol. 428(6983), pages 646-650, April.
    6. Dhaker Kroumi & Sabin Lessard, 2015. "Strong Migration Limit for Games in Structured Populations: Applications to Dominance Hierarchy and Set Structure," Games, MDPI, vol. 6(3), pages 1-29, September.
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    1. Qian, Jia-Li & Zhou, Yin-Xiang & Hao, Qing-Yi, 2024. "The emergence of cooperative behavior based on random payoff and heterogeneity of concerning social image," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).

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