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Memory-two strategies forming symmetric mutual reinforcement learning equilibrium in repeated prisoners’ dilemma game

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  • Ueda, Masahiko

Abstract

We investigate symmetric equilibria of mutual reinforcement learning when both players alternately learn the optimal memory-two strategies against the opponent in the repeated prisoners’ dilemma game. We provide a necessary condition for memory-two deterministic strategies to form symmetric equilibria. We then provide three examples of memory-two deterministic strategies which form symmetric mutual reinforcement learning equilibria. We also prove that mutual reinforcement learning equilibria formed by memory-two strategies are also mutual reinforcement learning equilibria when both players use reinforcement learning of memory-n strategies with n>2.

Suggested Citation

  • Ueda, Masahiko, 2023. "Memory-two strategies forming symmetric mutual reinforcement learning equilibrium in repeated prisoners’ dilemma game," Applied Mathematics and Computation, Elsevier, vol. 444(C).
    • Handle: RePEc:eee:apmaco:v:444:y:2023:i:c:s0096300322008876
    DOI: 10.1016/j.amc.2022.127819
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