Stochastic Fictitious Play using Particle Filters to update the beliefs of opponents strategies

Distributed optimization can be formulated as an n player coordination game. One of the most common learning techniques in game theory is fictitious play and its variations. However fictitious play is founded on an implicit assumption that opponents’ strategies are stationary. In this paper we present a new variation of fictitious play in which players predict opponents’ strategy using a particle filter algorithm. This allows us to use a more realistic model of opponent strategy. We used pre-specified opponents’ strategies to examine if our algorithm can efficiently track the strategies. Furthermore we have used these experiments to examine the impact of different values of our algorithm parameters on the results of strategy tracking. We then compared the results of the proposed algorithm with those of stochastic and dynamic fictitious play in a potential game and two climbing hill games, one with two players and the other with three players. Our algorithm converges more quickly to the optimum than both the competitor algorithms. Hence by placing a greater computational demand on the individual agents, less communication is required between the agents