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Inertia in spatial public goods games under weak selection

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  • Wang, Chaoqian
  • Szolnoki, Attila

Abstract

Due to limited cognitive skills for perceptual error or other emotional reasons, players may keep their current strategies even if there is a more promising choice. Such behavior inertia has already been studied, but its consequences remained unexplored in the weak selection limit. To fill this gap, we consider a spatial public goods game model where inertia is considered during the imitation process. By using the identity-by-descent method, we present analytical forms of the critical synergy factor r★, which determines when cooperation is favored. We find that inertia hinders cooperation, which can be explained by the decelerated coarsening process under weak selection. Interestingly, the critical synergy conditions for different updating protocols, including death-birth and birth-death rules, can be formally linked by the extreme limits of the inertia factor. To explore the robustness of our observations, calculations are made for different lattices and group sizes. Monte Carlo simulations also confirm the results.

Suggested Citation

  • Wang, Chaoqian & Szolnoki, Attila, 2023. "Inertia in spatial public goods games under weak selection," Applied Mathematics and Computation, Elsevier, vol. 449(C).
    • Handle: RePEc:eee:apmaco:v:449:y:2023:i:c:s0096300323001108
    DOI: 10.1016/j.amc.2023.127941
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    Cited by:

    1. Yu, Fengyuan & Wang, Jianwei & Chen, Wei & He, Jialu, 2023. "Increased cooperation potential and risk under suppressed strategy differentiation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 621(C).
    2. Yang, Zhengzhi & Zheng, Lei & Perc, Matjaž & Li, Yumeng, 2024. "Interaction state Q-learning promotes cooperation in the spatial prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 463(C).
    3. Xiaochen Wang & Lei Zhou & Alex McAvoy & Aming Li, 2023. "Imitation dynamics on networks with incomplete information," Nature Communications, Nature, vol. 14(1), pages 1-11, December.

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