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Zero-determinant strategies in repeated asymmetric games

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  • Taha, Mohammad A.
  • Ghoneim, Ayman

Abstract

Zero-determinant (ZD) strategies are conditional strategies which allow players adopting them to establish a relation between their expected payoffs and those of their opponents. The ZD strategies were investigated in different models including finite and infinite repeated two players’ games, multiplayer games, continuous action spaces and alternating move games. However, all previous studies considered only symmetric games between players, i.e., players have the same strategies and the same associated payoffs, thus the players’ identities are interchangeable without affecting the game's dynamics. In this study, we analytically model and derive the ZD strategies for asymmetric two players’ games, focusing on one-memory strategies and infinite repeated encounters. We derive the analytical bounds of equalizer and extortionate ZD strategies in 2 × 2 asymmetric games, which differ from the symmetric games case. Furthermore, we derive under what conditions a player using an extortionate ZD strategy will get a higher expected payoff than his/her opponent. Finally using a numerical example, we investigate ZD strategies in 2 × 2 asymmetric prisoner's dilemma game.

Suggested Citation

  • Taha, Mohammad A. & Ghoneim, Ayman, 2020. "Zero-determinant strategies in repeated asymmetric games," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    • Handle: RePEc:eee:apmaco:v:369:y:2020:i:c:s0096300319308549
    DOI: 10.1016/j.amc.2019.124862
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    References listed on IDEAS

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    1. EL-Seidy, Essam & Elshobaky, Entisarat.M. & Soliman, Karim.M., 2016. "Two population three-player prisoner’s dilemma game," Applied Mathematics and Computation, Elsevier, vol. 277(C), pages 44-53.
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    6. El-Seidy, Essam & Taha, Mohammad A., 2016. "The payoff matrix of repeated asymmetric 2×2 gamesAuthor-Name: Elshobaky, Entisarat M," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 393-402.
    7. McAvoy, Alex & Hauert, Christoph, 2017. "Autocratic strategies for alternating games," Theoretical Population Biology, Elsevier, vol. 113(C), pages 13-22.
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    Cited by:

    1. Zhou, Zhizhuo & Rong, Zhihai & Yang, Wen & Wu, Zhi-Xi, 2024. "Coevolution of extortion strategies with mixed imitation and aspiration learning dynamics in spatial Prisoner’s Dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    2. El-Salam, Salsabeel M. Abd & El-Seidy, Essam & Abdel-Malek, Amira R., 2023. "Evaluating zero-determinant strategies’ effects on cooperation and conflict resolution in repeated games," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. Kang, Kai & Tian, Jinyan & Zhang, Boyu, 2024. "Cooperation and control in asymmetric repeated games," Applied Mathematics and Computation, Elsevier, vol. 470(C).
    4. Jiali Wang & Changbing Tang & Jianquan Lu & Guanrong Chen, 2023. "Toward Zero-Determinant Strategies for Optimal Decision Making in Crowdsourcing Systems," Mathematics, MDPI, vol. 11(5), pages 1-21, February.
    5. Taha, Mohammad A. & Ghoneim, Ayman, 2021. "Zero-determinant strategies in infinitely repeated three-player prisoner's dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

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