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Distributed learning in a multi-agent potential game

In a non-cooperative dynamic game, each player participating in a changing environment aims to optimize its actions selfishly. In this paper, we focus our analysis on a class of games, namely dynamic potential game in multiagent systems. The problems of the game with constraints and without constraints are both considered; in both cases, we propose algorithms to learn the Nash equilibrium (NE) in a distributed fashion. The idea of NE learning is relied on two-time-scale dynamics and convex optimization. A numerical example is presented to verify the effectiveness of the proposed methods.