Decentralized Fictitious Play in Near-Potential Games with Time-Varying Communication Networks

We study the convergence properties of decentralized fictitious play (DFP)\nfor the class of near-potential games where the incentives of agents are nearly\naligned with a potential function. In DFP, agents share information only with\ntheir current neighbors in a sequence of time-varying networks, keep estimates\nof other agents' empirical frequencies, and take actions to maximize their\nexpected utility functions computed with respect to the estimated empirical\nfrequencies. We show that empirical frequencies of actions converge to a set of\nstrategies with potential function values that are larger than the potential\nfunction values obtained by approximate Nash equilibria of the closest\npotential game. This result establishes that DFP has identical convergence\nguarantees in near-potential games as the standard fictitious play in which\nagents observe the past actions of all the other agents.\n