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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. 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.
    2. Robert Sugden, 2005. "The Economics of Rights, Co-operation and Welfare," Palgrave Macmillan Books, Palgrave Macmillan, number 978-0-230-53679-1, September.
    3. 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.
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    Cited by:

    1. 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.
    2. Wettergren, Thomas A., 2021. "Replicator dynamics of an N-player snowdrift game with delayed payoffs," Applied Mathematics and Computation, Elsevier, vol. 404(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. 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).

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