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

Masahiko Ueda

Applied Mathematics and Computation, 2023, vol. 444, issue C

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.

Keywords: Repeated prisoners’ dilemma game; Reinforcement learning; Memory-two strategies (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:444:y:2023:i:c:s0096300322008876

DOI: 10.1016/j.amc.2022.127819

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