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Delayed response in the Hawk Dove game

Author

Listed:
  • James Burridge

    (University of Portsmouth)

  • Yu Gao

    (School of Physics and Astronomy, University of Nottingham)

  • Yong Mao

    (School of Physics and Astronomy, University of Nottingham)

Abstract

We consider a group of agents playing the Hawk-Dove game. These agents have a finite memory of past interactions which they use to optimize their play. By both analytical and numerical approaches, we show that an instability occurs at a critical memory length, and we provide its characterization. We show also that when the game is stable, having a long memory is beneficial but that instability, which may be produced by excessively long memory, hands the advantage to those with shorter memories.

Suggested Citation

  • James Burridge & Yu Gao & Yong Mao, 2017. "Delayed response in the Hawk Dove game," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(1), pages 1-6, January.
    • Handle: RePEc:spr:eurphb:v:90:y:2017:i:1:d:10.1140_epjb_e2016-70471-1
    DOI: 10.1140/epjb/e2016-70471-1
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    References listed on IDEAS

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    1. Robert Sugden, 2005. "Rights, Co-operation and Welfare," Palgrave Macmillan Books, in: The Economics of Rights, Co-operation and Welfare, chapter 9, pages 170-182, Palgrave Macmillan.
    2. Robert Sugden, 2005. "The Economics of Rights, Co-operation and Welfare," Palgrave Macmillan Books, Palgrave Macmillan, number 978-0-230-53679-1, October.
    3. Ding, Fei & Liu, Yun & Shen, Bo & Si, Xia-Meng, 2010. "An evolutionary game theory model of binary opinion formation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(8), pages 1745-1752.
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    Cited by:

    1. Wettergren, Thomas A., 2021. "Replicator dynamics of an N-player snowdrift game with delayed payoffs," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    2. Yuan, Hairui & Meng, Xinzhu, 2022. "Replicator dynamics of division of labor games with delayed payoffs in infinite populations," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    3. Wettergren, Thomas A., 2023. "Replicator dynamics of evolutionary games with different delays on costs and benefits," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    4. Burridge, James & Gnacik, Michał, 2022. "Public efforts to reduce disease transmission implied from a spatial game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    5. Chongyi Zhong & Hui Yang & Zixin Liu & Juanyong Wu, 2020. "Stability of Replicator Dynamics with Bounded Continuously Distributed Time Delay," Mathematics, MDPI, vol. 8(3), pages 1-12, March.

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