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We study a subclass of $n$-player stochastic games, namely, stochastic gameswith independent chains and unknown transition matrices. In this class ofgames, players control their own internal Markov chains whose transitions donot depend on the states/actions of other players. However, players' decisionsare coupled through their payoff functions. We assume players can receive onlyrealizations of their payoffs, and that the players can not observe the statesand actions of other players, nor do they know the transition probabilitymatrices of their own Markov chain. Relying on a compact dual formulation ofthe game based on occupancy measures and the technique of confidence set tomaintain high-probability estimates of the unknown transition matrices, wepropose a fully decentralized mirror descent algorithm to learn an$\epsilon$-NE for this class of games. The proposed algorithm has the desiredproperties of independence, scalability, and convergence. Specifically, underno assumptions on the reward functions, we show the proposed algorithmconverges in polynomial time in a weaker distance (namely, the averagedNikaido-Isoda gap) to the set of $\epsilon$-NE policies with arbitrarily highprobability. Moreover, assuming the existence of a variationally stable Nashequilibrium policy, we show that the proposed algorithm convergesasymptotically to the stable $\epsilon$-NE policy with arbitrarily highprobability. In addition to Markov potential games and linear-quadraticstochastic games, this work provides another subclass of $n$-player stochasticgames that, under some mild assumptions, admit polynomial-time learningalgorithms for finding their stationary $\epsilon$-NE policies.

Scalable and Independent Learning of Nash Equilibrium Policies in $n$-Player Stochastic Games with Unknown Independent Chains