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Kinetic approach to the collective dynamics of the rock-paper-scissors binary game

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  • Pouradier Duteil, Nastassia
  • Salvarani, Francesco

Abstract

This article studies the kinetic dynamics of the rock-paper-scissors binary game. We first prove existence and uniqueness of the solution of the kinetic equation and subsequently we prove the rigorous derivation of the quasi-invariant limit for two meaningful choices of the domain of definition of the independent variables. We notice that the domain of definition of the problem plays a crucial role and heavily influences the behavior of the solution. The rigorous proof of the relaxation limit does not need the use of entropy estimates for ensuring compactness.

Suggested Citation

  • Pouradier Duteil, Nastassia & Salvarani, Francesco, 2021. "Kinetic approach to the collective dynamics of the rock-paper-scissors binary game," Applied Mathematics and Computation, Elsevier, vol. 388(C).
    • Handle: RePEc:eee:apmaco:v:388:y:2021:i:c:s0096300320304549
    DOI: 10.1016/j.amc.2020.125496
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    References listed on IDEAS

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    1. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, December.
    2. repec:fth:iniesr:487 is not listed on IDEAS
    3. Iwamura, Yoshiro & Nagashima, Keisuke & Tanimoto, Jun, 2020. "Evolutionary dynamics of a 3-strategy game: Cooperator, defector and costly cooperative loner strategic types," Applied Mathematics and Computation, Elsevier, vol. 370(C).
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    Cited by:

    1. Wang, Xianjia & Liu, Ke & Yang, Zhipeng, 2025. "Strategy evolution of network conformists and rational imitators in the rock–paper–scissors game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 669(C).
    2. Zhong, Yue & Lai, Shaoyong & Hu, Chunhua, 2021. "Investigations to the dynamics of wealth distribution in a kinetic exchange model," Applied Mathematics and Computation, Elsevier, vol. 404(C).

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