arXiv AI By Hisato Komatsu

Symmetric solution of the Bellman optimality equation for repeated harmony game

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The paper presents a symmetric solution to the Bellman optimality equation for a repeated harmony game, revealing three distinct symmetric solutions. One solution corresponds to the trivial All‑Cooperate strategy, another aligns with the Win‑stay Lose‑shift strategy known from the prisoner's dilemma, and a third nontrivial strategy is explored in detail. The authors also numerically examine which of these strategies agents learn using a reinforcement learning algorithm.

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