Memory-two strategies forming symmetric mutual reinforcement learning equilibrium in repeated prisoner's dilemma game
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We investigate symmetric equilibria of mutual reinforcement learning when both players alternately learn the optimal memory-two strategies against the opponent in the repeated prisoner's dilemma game. We provide the necessary condition for memory-two deterministic strategies to form symmetric equilibria. We then provide two 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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