Cyclic Equilibria in Markov Games

Part of Advances in Neural Information Processing Systems 18 (NIPS 2005)

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Authors

Martin Zinkevich, Amy Greenwald, Michael Littman

Abstract

Although variants of value iteration have been proposed for finding Nash or correlated equilibria in general-sum Markov games, these variants have not been shown to be effective in general. In this paper, we demon- strate by construction that existing variants of value iteration cannot find stationary equilibrium policies in arbitrary general-sum Markov games. Instead, we propose an alternative interpretation of the output of value it- eration based on a new (non-stationary) equilibrium concept that we call “cyclic equilibria.” We prove that value iteration identifies cyclic equi- libria in a class of games in which it fails to find stationary equilibria. We also demonstrate empirically that value iteration finds cyclic equilibria in nearly all examples drawn from a random distribution of Markov games.