An extremum seeking algorithm for monotone Nash equilibrium problems

TL;DR

This paper introduces a new extremum seeking algorithm designed to find Nash equilibria in monotone games using only zeroth-order feedback, with proven convergence properties and demonstrated effectiveness through simulations.

Contribution

The paper proposes a novel extremum seeking algorithm based on hybrid system theory that converges to Nash equilibria in monotone pseudogradient games, addressing limitations of standard methods.

Findings

The proposed algorithm successfully converges to Nash equilibria in simulations.

Standard extremum seeking algorithms fail in the tested scenarios.

The method effectively handles allocation problems with fixed demand.

Abstract

In this paper we consider the problem of finding a Nash equilibrium (NE) via zeroth-order feedback information in games with merely monotone pseudogradient mapping. Based on hybrid system theory, we propose a novel extremum seeking algorithm which converges to the set of Nash equilibria in a semi-global practical sense. Finally, we present two simulation examples. The first shows that the standard extremum seeking algorithm fails, while ours succeeds in reaching NE. In the second, we simulate an allocation problem with fixed demand.