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Limiting Dynamics for Q-Learning with Memory One in Symmetric Two-Player, Two-Action Games

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  • J. M. Meylahn
  • L. Janssen
  • Hassan Zargarzadeh

Abstract

We develop a method based on computer algebra systems to represent the mutual pure strategy best-response dynamics of symmetric two-player, two-action repeated games played by players with a one-period memory. We apply this method to the iterated prisoner’s dilemma, stag hunt, and hawk-dove games and identify all possible equilibrium strategy pairs and the conditions for their existence. The only equilibrium strategy pair that is possible in all three games is the win-stay, lose-shift strategy. Lastly, we show that the mutual best-response dynamics are realized by a sample batch Q-learning algorithm in the infinite batch size limit.

Suggested Citation

  • J. M. Meylahn & L. Janssen & Hassan Zargarzadeh, 2022. "Limiting Dynamics for Q-Learning with Memory One in Symmetric Two-Player, Two-Action Games," Complexity, Hindawi, vol. 2022, pages 1-20, November.
    • Handle: RePEc:hin:complx:4830491
    DOI: 10.1155/2022/4830491
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    Cited by:

    1. Ding, Zhen-Wei & Zheng, Guo-Zhong & Cai, Chao-Ran & Cai, Wei-Ran & Chen, Li & Zhang, Ji-Qiang & Wang, Xu-Ming, 2023. "Emergence of cooperation in two-agent repeated games with reinforcement learning," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Gao, Meng & Li, Zhi & Wu, Te, 2023. "Evolutionary dynamics of friendship-driven reputation strategies," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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