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.Comment: 5 pages, 1 figure, to appear in Proceedings of Asilomar Conference on Signals, Systems, and Computer

Decentralized Inertial Best-Response with Voluntary and Limited Communication in Random Communication Networks

Multiple autonomous agents interact over a random communication network to maximize their individual utility functions which depend on the actions of other agents. We consider decentralized best-response with inertia type algorithms in which agents form beliefs about the future actions of other players based on local information, and take an action that maximizes their expected utility computed with respect to these beliefs or continue to take their previous action. We show convergence of these types of algorithms to a Nash equilibrium in weakly acyclic games under the condition that the belief update and information exchange protocols successfully learn the actions of other players with positive probability in finite time given a static environment, i.e., when other agents' actions do not change. We design a decentralized fictitious play algorithm with voluntary and limited communication (DFP-VL) protocols that satisfy this condition. In the voluntary communication protocol, each agent decides whom to exchange information with by assessing the novelty of its information and the potential effect of its information on others' assessments of their utility functions. The limited communication protocol entails agents sending only their most frequent action to agents that they decide to communicate with. Numerical experiments on a target assignment game demonstrate that the voluntary and limited communication protocol can more than halve the number of communication attempts while retaining the same convergence rate as DFP in which agents constantly attempt to communicate.Comment: 10 page