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arXiv · 2304.03052

Generalized uncertain Nash games: Reformulation and robust equilibrium seeking -- Extended version

Marta Fochesato·Filippo Fabiani·John Lygeros
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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

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Marta Fochesato, Filippo Fabiani, John Lygeros. 2023-04-06. Generalized uncertain Nash games: Reformulation and robust equilibrium seeking -- Extended version. https://arxiv.org/abs/2304.03052

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