2023/05/23 by Fivos Kalogiannis, Ioannis Panageas, Kalogiannis, Fivos +1
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #Computer Science and Game Theory (cs.GT) #Experimental Behavioral Economics Studies #FOS: Computer and information sciences #Game Theory and Applications #Game Theory and Voting Systems #Multiagent Systems (cs.MA) #Social and Information Networks (cs.SI)
paper · pdf · doi:10.48550/arxiv.2305.14329
openalex publication_date 2023/05/23 · openalex created_date 2023/05/27 · openalex updated_date 2026/07/28
The works of (Daskalakis et al., 2009, 2022; Jin et al., 2022; Deng et al., 2023) indicate that computing Nash equilibria in multi-player Markov games is a computationally hard task. This fact raises the question of whether or not computational intractability can be circumvented if one focuses on specific classes of Markov games. One such example is two-player zero-sum Markov games, in which efficient ways to compute a Nash equilibrium are known. Inspired by zero-sum polymatrix normal-form games (Cai et al., 2016), we define a class of zero-sum multi-agent Markov games in which there are only pairwise interactions described by a graph that changes per state. For this class of Markov games, we show that an ε-approximate Nash equilibrium can be found efficiently. To do so, we generalize the techniques of (Cai et al., 2016), by showing that the set of coarse-correlated equilibria collapses to the set of Nash equilibria. Afterwards, it is possible to use any algorithm in the literature that computes approximate coarse-correlated equilibria Markovian policies to get an approximate Nash equilibrium.