Markov $\alpha$-Potential Games: Equilibrium Approximation and Regret Analysis

This paper proposes a new notion of Markov α-potential games to study Markov games. Two important classes of practically significant Markov games, Markov congestion games and the perturbed Markov team games, are analyzed in this framework of Markov α-potential games, with explicit characterization of the upper bound for α and its relation to game parameters. Moreover, any maximizer of the α-potential function is shown to be an α-stationary Nash equilibrium of the game. Furthermore, two algorithms for the Nash regret analysis, namely the projected gradient-ascent algorithm and the sequential maximum improvement algorithm, are presented and corroborated by numerical experiments. Key words: Markov α-potential games; Markov potential games; Multi-agent reinforcement learning; Nash-regret; Markov congestion games; Perturbed Markov team games; Projected gradient-ascent algorithm; Sequential maximum improvement.