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

TL;DR

This paper develops a distributed algorithm to find approximate Bayesian Nash equilibria in continuous-type subnetwork zero-sum games, addressing challenges of infinite-dimensional strategy spaces and communication constraints.

Contribution

It introduces a discretization and compression-based method to efficiently compute approximate BNEs with provable error bounds and convergence rates.

Findings

Proposed a discretization scheme with explicit error bounds.

Designed a compression scheme ensuring unbiased estimations.

Achieved an $O(rac{ ext{ln} T}{ ext{sqrt} T})$ convergence rate.

Abstract

In this paper, we consider a continuous-type Bayesian Nash equilibrium (BNE) seeking problem in subnetwork zero-sum games, which is a generalization of deterministic subnetwork zero-sum games and discrete-type Bayesian zero-sum games. In this continuous-type 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 non-compact set and convey such complex strategies in network communication. To this end, we design two steps to overcome the above bottleneck. 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 one 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 compressed communication. Based on the above two steps, we propose a distributed communication-efficient algorithm to practicably seek an approximate BNE, and further provide an explicit error bound and an $O(\ln T/\sqrt{T})$ convergence rate.