Bayesian Graphical Games for Synchronization in Dynamical Systems

Abstract

In this paper, differential games with incomplete information, or Bayesian games, are formulated for a set of continuous-time dynamical systems linked together by a communication graph. These new Bayesian graphical games for dynamical systems represent the situation where the agents are uncertain about their actual payoff and must collect additional information to improve their estimation of the real setting of their environment. Furthermore, the agents play their best response strategies with respect to the policies of their neighbors. A tight relationship between the beliefs of an agent and his distributed best response policy is obtained. Conditions for the so-called Bayes-Nash equilibrium are provided. A distributed belief update algorithm is developed that does not require the full knowledge of graph topology.