Distributed Algorithm for Seeking Bayesian Nash Equilibrium in Subnetwork Zero-sum Games

In this paper, we consider a Bayesian Nash equilibrium seeking problem in subnetwork zero-sum games. The network consists of two subnetworks and agents in the same subnetwork collaborate to compete with other agents in the adversarial subnetwork. Each agent has its own cost function and receives information from neighbors through time-varying graphs. We propose a distributed algorithm for seeking a Bayesian Nash equilibrium and analyze the convergence when the graphs are uniformly jointly strongly connected, and the cost functions are strictly convex. We illustrate the effectiveness of the proposed algorithm by a numerical example.