Distributed Algorithm for Continuous-Type Bayesian Nash Equilibrium in Subnetwork Zero-Sum Games

In this article, we consider a continuous-type Bayesian Nash equilibrium (BNE) seeking problem in subnetwork zero-sum games, which is a generalization of either deterministic subnetwork zero-sum games or discrete-type Bayesian zero-sum games. In this model, because the feasible strategy set is composed of infinite-dimensional functions and is not compact, it is hard to seek a BNE in a noncompact set and convey such complex strategies in network communication. To this end, we give a two-step design. One is a discretization step, where we discretize continuous types and prove that the BNE of the discretized model is an approximate BNE of the continuous model with an explicit error bound. The other is a communication step, where we adopt a novel compression scheme with a designed sparsification rule and prove that agents can obtain unbiased estimations through the compressed communication. Based on the two steps, we propose a distributed communication-efficient algorithm to practically seek an approximate BNE, and further provide the convergence analysis and explicit error bounds.