On the robustness of equilibria in generalized aggregative games

We assess the robustness of equilibria in generalized Nash equilibrium problems in aggregative form subject to linear coupling constraints affected by uncertainty with a possibly unknown probability distribution. Within a data-driven context, we apply the scenario approach paradigm to provide a-post...

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Bibliographic Details
Published inProceedings of the IEEE Conference on Decision & Control pp. 3725 - 3730
Main Authors Fabiani, Filippo, Margellos, Kostas, Goulart, Paul J.
Format Conference Proceeding
LanguageEnglish
Published IEEE 14.12.2020
Subjects
Couplings
Games
Nash equilibrium
Probabilistic logic
Probability distribution
Robustness
Uncertainty
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ISSN2576-2370
DOI10.1109/CDC42340.2020.9304348

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Summary:We assess the robustness of equilibria in generalized Nash equilibrium problems in aggregative form subject to linear coupling constraints affected by uncertainty with a possibly unknown probability distribution. Within a data-driven context, we apply the scenario approach paradigm to provide a-posteriori feasibility certificates for the entire set of generalized Nash equilibria of the game. We then show that assessing the violation probability of such a set only requires one to enumerate the constraints that "shape" it. For the class of aggregative games, this results in solving a feasibility problem on each active facet of the feasibility region, for which we propose a semi-decentralized, structure-preserving algorithm.
ISSN:2576-2370
DOI:10.1109/CDC42340.2020.9304348