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.
On the robustness of equilibria in generalized aggregative games
Fabiani, Filippo;
2020-01-01
Abstract
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.File | Dimensione | Formato | |
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