Memory-two Strategies Forming Symmetric Mutual Reinforcement Learning Equilibrium In Repeated Prisoners' Dilemma Game

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 \(n>2\).

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