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This paper presents a decentralized learning algorithm for stochastic games,also known as Markov games (MGs). The algorithm is radically uncoupled,model-free, rational, and convergent by reaching near equilibrium in two-agentzero-sum and identical-interest MGs, and certain multi-agent general-sum MGsfor both discounted and time-averaged cases. The paper introducesadditive-reward product (ARP) games as a new class of Markov games to addressconvergence beyond zero-sum and identical-interest cases. In ARP games, stateis a composition of local states, each local state determines the rewards in anadditive way and they get controlled by a single agent. The algorithm canconverge almost surely to near equilibrium in general-sum ARP games, providedthat the strategic-form games induced by the immediate rewards arestrategically equivalent to either two-agent zero-sum or potential games. Theapproximation errors in the results decay with the episode length and theconvergence results can be generalized to the cases with more than two agentsif the strategic-form games induced by the rewards are polymatrix games.

Decentralized Learning for Stochastic Games: Beyond Zero Sum and Identical Interest