Actor-Critic Fictitious Play in Simultaneous Move Multistage Games

Fictitious play is a game theoretic iterative procedure meant to learn an equilibrium in normal form games. However, this algorithm requires that each player has full knowledge of other players’ strategies. Using an architecture inspired by actor-critic algorithms, we build a stochastic approximation of the fictitious play process. This procedure is on-line, decentralized (an agent has no information of others’ strategies and rewards) and applies to multistage games (a generalization of normal form games). In addition, we prove convergence of our method towards a Nash equilibrium in both the cases of zero-sum two-player multistage games and cooperative multistage games. We also provide empirical evidence of the soundness of our approach on the game of Alesia with and without function approximation.