Payoff-Based Approach to Learning Nash Equilibria in Convex Games

TL;DR

This paper introduces a distributed payoff-based algorithm enabling agents in convex games to learn Nash equilibria using only their current cost information, with proven convergence and demonstrated effectiveness.

Contribution

It presents a novel payoff-based learning algorithm for Nash equilibria in convex games, requiring minimal information and ensuring convergence.

Findings

Algorithm converges to Nash equilibrium

Proven convergence using stochastic process theory

Numerical case study validates performance

Abstract

We consider multi-agent decision making, where each agent optimizes its cost function subject to constraints. Agents' actions belong to a compact convex Euclidean space and the agents' cost functions are coupled. We propose a distributed payoff-based algorithm to learn Nash equilibria in the game between agents. Each agent uses only information about its current cost value to compute its next action. We prove convergence of the proposed algorithm to a Nash equilibrium in the game leveraging established results on stochastic processes. The performance of the algorithm is analyzed with a numerical case study.