Learning equilibria with personalized incentives in a class of nonmonotone games

TL;DR

This paper introduces a two-layer scheme for finding equilibria in nonmonotone generalized Nash games using personalized incentives and noisy feedback, even when the potential function is unavailable.

Contribution

It proposes a novel Nash equilibrium seeking algorithm leveraging personalized incentives and noisy feedback, applicable to nonmonotone games without explicit potential functions.

Findings

Algorithm converges to equilibrium with standard learning policies.

Numerical experiments validate effectiveness in hypomonotone games.

Personalized incentives improve equilibrium computation in complex games.

Abstract

We consider quadratic, nonmonotone generalized Nash equilibrium problems with symmetric interactions among the agents. Albeit this class of games is known to admit a potential function, its formal expression can be unavailable in several real-world applications. For this reason, we propose a two-layer Nash equilibrium seeking scheme in which a central coordinator exploits noisy feedback from the agents to design personalized incentives for them. By making use of those incentives, the agents compute a solution to an extended game, and then return feedback measures to the coordinator. We show that our algorithm returns an equilibrium if the coordinator is endowed with standard learning policies, and corroborate our results on a numerical instance of a hypomonotone game.