\Epsilon$ Nash Equilibrium

Epsilon (ε)-Nash equilibrium represents a strategy profile in a game where no player can improve their payoff by more than ε by unilaterally changing their strategy. Current research focuses on developing algorithms to efficiently compute ε-Nash equilibria, particularly in complex settings like quantum games, multi-agent reinforcement learning, and mean-field games, employing methods such as log-linear learning, matrix multiplicative weight updates, and natural policy gradients. These advancements are significant for improving the tractability of game-theoretic analysis and enabling the design of more robust and efficient algorithms for multi-agent systems in various applications, including online advertising and resource allocation. The exploration of structural properties of games, like polymatrix decomposability, also aims to provide performance guarantees for self-play learning algorithms.