Optimal selection and tracking of generalized Nash equilibria in monotone games

TL;DR

This paper addresses the challenge of computing an optimal generalized Nash equilibrium in monotone games by developing distributed algorithms that select and track the most efficient equilibrium, even in dynamic environments.

Contribution

It introduces a novel approach leveraging fixed-point selection theory to compute and track optimal GNEs in monotone and time-varying games.

Findings

Distributed algorithms successfully compute optimal GNEs

Algorithms extend to time-varying game settings

Asymptotic tracking error depends on agents' computational capabilities

Abstract

A fundamental open problem in monotone game theory is the computation of a specific generalized Nash equilibrium (GNE) among all the available ones, e.g. the optimal equilibrium with respect to a system-level objective. The existing GNE seeking algorithms have in fact convergence guarantees toward an arbitrary, possibly inefficient, equilibrium. In this paper, we solve this open problem by leveraging results from fixed-point selection theory and in turn derive distributed algorithms for the computation of an optimal GNE in monotone games. We then extend the technical results to the time-varying setting and propose an algorithm that tracks the sequence of optimal equilibria up to an asymptotic error, whose bound depends on the local computational capabilities of the agents.