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Impact of individual sensitivity to payoff difference between individuals on a discrete-time imitation dynamics

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  • Wang, Si-Yi
  • Feng, Tian-Jiao
  • Tao, Yi
  • Wu, Jia-Jia

Abstract

The impact of individual sensitivity to the difference between expected payoffs of individuals interacting in pairs on a discrete-time imitation dynamics was investigated, where the probability of mutual imitation between pairs of individuals is measured by the Fermi function. The main results show clearly that although the evolutionary stability of our model is independent of the individual sensitivity, the change of this sensitivity may profoundly affect the dynamical behavior of the system, for example, the periodic or chaotic fluctuations due to increased individual sensitivity. These results may be more helpful for us to understand the imitation dynamics in real systems.

Suggested Citation

  • Wang, Si-Yi & Feng, Tian-Jiao & Tao, Yi & Wu, Jia-Jia, 2023. "Impact of individual sensitivity to payoff difference between individuals on a discrete-time imitation dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    • Handle: RePEc:eee:chsofr:v:166:y:2023:i:c:s096007792201092x
    DOI: 10.1016/j.chaos.2022.112913
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    References listed on IDEAS

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    1. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
    2. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
    3. James C. Felli & Gordon B. Hazen, 1998. "Sensitivity Analysis and the Expected Value of Perfect Information," Medical Decision Making, , vol. 18(1), pages 95-109, January.
    4. Hu, Wenjun & Zhang, Gang & Tian, Haiyan, 2019. "The stability of imitation dynamics with discrete distributed delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 218-224.
    5. Brit Grosskopf & Ido Erev & Eldad Yechiam, 2006. "Foregone with the Wind: Indirect Payoff Information and its Implications for Choice," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(2), pages 285-302, August.
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    Cited by:

    1. Wang, Si-Yi & Wang, Qing-Lian & Zhang, Xiao-Wei & Wang, Rui-Wu, 2023. "Evolutionary cooperation dynamics of combining imitation and super-rational aspiration induced strategy updating," Applied Mathematics and Computation, Elsevier, vol. 456(C).

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