Generalized uncertain Nash games: Reformulation and robust equilibrium seeking -- Extended version
Abstract
We consider generalized Nash equilibrium problems (GNEPs) with linear coupling constraints affected by both local (i.e., agent-wise) and global (i.e., shared resources) disturbances taking values in polyhedral uncertainty sets. By making use of traditional tools borrowed from robust optimization, for this class of problems we derive a tractable, finite-dimensional reformulation leading to a deterministic ''extended game'', and we show that this latter still amounts to a GNEP featuring generalized Nash equilibria ''in the worst-case''. We then design a fully-distributed, accelerated algorithm based on monotone operator theory, which enjoys convergence towards a Nash equilibrium of the original, uncertain game under weak structural assumptions. Finally, we illustrate the effectiveness of the proposed distributed scheme through numerical simulations
Keywords
Cite
@article{arxiv.2304.03052,
title = {Generalized uncertain Nash games: Reformulation and robust equilibrium seeking -- Extended version},
author = {Marta Fochesato and Filippo Fabiani and John Lygeros},
journal= {arXiv preprint arXiv:2304.03052},
year = {2023}
}
Comments
Accepted at European Control Conference (ECC) 2023