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Policy gradient methods enjoy strong practical performance in numerous tasksin reinforcement learning. Their theoretical understanding in multiagentsettings, however, remains limited, especially beyond two-player competitiveand potential Markov games. In this paper, we develop a new framework tocharacterize optimistic policy gradient methods in multi-player Markov gameswith a single controller. Specifically, under the further assumption that thegame exhibits an equilibrium collapse, in that the marginals of coarsecorrelated equilibria (CCE) induce Nash equilibria (NE), we show convergence tostationary $\epsilon$-NE in $O(1/\epsilon^2)$ iterations, where $O(\cdot)$suppresses polynomial factors in the natural parameters of the game. Such anequilibrium collapse is well-known to manifest itself in two-player zero-sumMarkov games, but also occurs even in a class of multi-player Markov games withseparable interactions, as established by recent work. As a result, we bypassknown complexity barriers for computing stationary NE when either of ourassumptions fails. Our approach relies on a natural generalization of theclassical Minty property that we introduce, which we anticipate to have furtherapplications beyond Markov games.

Optimistic Policy Gradient in Multi-Player Markov Games with a Single Controller: Convergence Beyond the Minty Property