Optimal Selection and Tracking of Generalized Nash Equilibria in Monotone Games

Journal article (2023)

Authors

E. Benenati Team Sergio Grammatico - Mechanical, Maritime and Materials Engineering
W. Ananduta Team Sergio Grammatico - Mechanical, Maritime and Materials Engineering
S. Grammatico , Team Sergio Grammatico - Mechanical, Maritime and Materials Engineering
Research Group
Team Sergio Grammatico (Mechanical, Maritime and Materials Engineering) (TU Delft)
Copyright: © 2023 E. Benenati, W. Ananduta, S. Grammatico
DOI: https://doi.org/10.1109/TAC.2023.3288372
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Published Date

2023

Language

English

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Sergio Grammatico

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.

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