Efficient Distributed Learning in Stochastic Non-cooperative Games without Information Exchange

TL;DR

This paper introduces a novel distributed learning algorithm for stochastic non-cooperative games that eliminates the need for inter-player communication, using gradient estimation and mirror descent to efficiently find Nash equilibria.

Contribution

The paper presents a communication-free stochastic distributed learning algorithm for Nash equilibrium computation in non-cooperative games, with proven convergence and improved rates.

Findings

Converges to Nash equilibrium in mean square for strictly monotone games.

Faster convergence rate than existing algorithms.

Validated effectiveness through numerical experiments.

Abstract

In this work, we study stochastic non-cooperative games, where only noisy black-box function evaluations are available to estimate the cost function for each player. Since each player's cost function depends on both its own decision variables and its rivals' decision variables, local information needs to be exchanged through a center/network in most existing work for seeking the Nash equilibrium. We propose a new stochastic distributed learning algorithm that does not require communications among players. The proposed algorithm uses simultaneous perturbation method to estimate the gradient of each cost function, and uses mirror descent method to search for the Nash equilibrium. We provide asymptotic analysis for the bias and variance of gradient estimates, and show the proposed algorithm converges to the Nash equilibrium in mean square for the class of strictly monotone games at a rate faster than the existing algorithms. The effectiveness of the proposed method is buttressed in a numerical experiment.