On the robustness of equilibria in generalized aggregative games - Fabiani, Filippo; Margellos, Kostas; Goulart, Paul J. (Proceedings of the IEEE Conference on Decision & Control, 2020)
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.