This paper addresses the problem of learning a Nash equilibrium in $γ$-discounted multiplayer general-sum Markov Games (MGs) in a batch setting. As the number of players increases in MG, the agents may either collaborate or team apart to increase their final rewards. One solution to address this problem is to look for a Nash equilibrium. Although, several techniques were found for the subcase of two-player zero-sum MGs, those techniques fail to find a Nash equilibrium in general-sum Markov Games. In this paper, we introduce a new definition of $ε$-Nash equilibrium in MGs which grasps the strategy’s quality for multiplayer games. We prove that minimizing the norm of two Bellman-like residuals implies to learn such an $ε$-Nash equilibrium. Then, we show that minimizing an empirical estimate of the $L_p$ norm of these Bellman-like residuals allows learning for general-sum games within the batch setting. Finally, we introduce a neural network architecture that successfully learns a Nash equilibrium in generic multiplayer general-sum turn-based MGs.
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