On the complexity of computing Markov perfect equilibrium in general-sum stochastic games.

Similar to the role of Markov decision processes in reinforcement learning, Markov games (also called stochastic games) lay down the foundation for the study of multi-agent reinforcement learning and sequential agent interactions. We introduce approximate Markov perfect equilibrium as a solution to the computational problem of finite-state stochastic games repeated in the infinite horizon and prove its PPAD -completeness. This solution concept preserves the Markov perfect property and opens up the possibility for the success of multi-agent reinforcement learning algorithms on static two-player games to be extended to multi-agent dynamic games, expanding the reign of the PPAD -complete class.
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