Bayesian Nash Equilibrium Seeking for Distributed Incomplete-information Aggregative Games

TL;DR

This paper develops a distributed algorithm to find approximate Bayesian Nash equilibria in incomplete-information aggregative games, addressing the challenges of infinite-dimensional strategy spaces and type continuity.

Contribution

It introduces a discretization approach for continuous types and proposes a convergent distributed algorithm for $oldsymbol{ ext{ extepsilon}}$-BNE in such games.

Findings

Discretization yields an $ ext{ extepsilon}$-BNE approximation.

Proposed algorithm converges to the $ ext{ extepsilon}$-BNE.

Addresses aggregation function handling in incomplete-information settings.

Abstract

In this paper, we consider a distributed Bayesian Nash equilibrium (BNE) seeking problem in incomplete-information aggregative games, which is a generalization of Bayesian games and deterministic aggregative games. We handle the aggregation function for distributed incomplete-information situations. Since the feasible strategies are infinite-dimensional functions and lie in a non-compact set, the continuity of types brings barriers to seeking equilibria. To this end, we discretize the continuous types and then prove that the equilibrium of the derived discretized model is an $\epsilon$-BNE. On this basis, we propose a distributed algorithm for an $\epsilon$-BNE and further prove its convergence.