Distributed Fictitious Play in Potential Games with Time Varying Communication Networks

We propose a distributed algorithm for multiagent systems that aim to optimize a common objective when agents differ in their estimates of the objective-relevant state of the environment. Each agent keeps an estimate of the environment and a model of the behavior of other agents. The model of other agents’ behavior assumes agents choose their actions randomly based on a stationary distribution determined by the empirical frequencies of past actions. At each step, each agent takes the action that maximizes its expectation of the common objective computed with respect to its estimate of the environment and its model of others. We propose a weighted averaging rule with non-doubly stochastic weights for agents to estimate the empirical frequency of past actions of all other agents by exchanging their estimates with their neighbors over a time-varying communication network. Under this averaging rule, we show agents’ estimates converge to the actual empirical frequencies fast enough. This implies convergence of actions to a Nash equilibrium of the game with identical payoffs given by the expectation of the common objective with respect to an asymptotically agreed estimate of the state of the environment.