Markov α-Potential Games
arxiv(2023)
摘要
This paper proposes a new framework of Markov α-potential games to
study Markov games. In this new framework, Markov games are shown to be Markov
α-potential games, and the existence of an associated α-potential
function is established. Any optimizer of an α-potential function is
shown to be an α-stationary NE. Two important classes of practically
significant Markov games, Markov congestion games and the perturbed Markov team
games, are studied via this framework of Markov α-potential games, with
explicit characterization of an upper bound for α and its relation to
game parameters. Additionally, a semi-infinite linear programming based
formulation is presented to obtain an upper bound for α for any Markov
game. Furthermore, two equilibrium approximation algorithms, namely the
projected gradient-ascent algorithm and the sequential maximum improvement
algorithm, are presented along with their Nash regret analysis, and
corroborated by numerical experiments.
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