Distributed Stochastic Nash Equilibrium Learning in Locally Coupled Network Games with Unknown Parameters

TL;DR

This paper introduces a distributed learning algorithm for stochastic Nash equilibrium problems in locally coupled network games with unknown parameters, ensuring convergence under certain conditions.

Contribution

It develops a novel distributed proximal-point and least-squares based algorithm for learning unknown parameters and equilibria in complex network games.

Findings

Algorithm converges almost surely to Nash equilibria.

Effective in environments with multi-dimensional unknown parameters.

Applicable to locally coupled network games with uncertain dynamics.

Abstract

In stochastic Nash equilibrium problems (SNEPs), it is natural for players to be uncertain about their complex environments and have multi-dimensional unknown parameters in their models. Among various SNEPs, this paper focuses on locally coupled network games where the objective of each rational player is subject to the aggregate influence of its neighbors. We propose a distributed learning algorithm based on the proximal-point iteration and ordinary least-square estimator, where each player repeatedly updates the local estimates of neighboring decisions, makes its augmented best-response decisions given the current estimated parameters, receives the realized objective values, and learns the unknown parameters. Leveraging the Robbins-Siegmund theorem and the law of large deviations for M-estimators, we establish the almost sure convergence of the proposed algorithm to solutions of SNEPs when the updating step sizes decay at a proper rate.