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In this paper a distribution-free methodology is presented for providingrobustness guarantees for Nash equilibria (NE) of multi-agent games. Leveragingrecent a posteriori developments of the so called scenario approach (Campi etal., 2018), we provide probabilistic guarantees for feasibility problems withpolytopic constraints. This result is then used in the context of multi-agentgames, allowing to provide robustness certificates for constraint violation ofany NE of a given game. Our guarantees can be used alongside any NE seekingalgorithm that returns some equilibrium solution. Finally, by exploiting thestructure of our problem, we circumvent the need of employing computationallyprohibitive algorithms to find an irreducible support subsample, a concept atthe core of the scenario approach. Our theoretical results are accompanied bysimulation studies that investigate the robustness of the solutions of twodifferent problems, namely, a 2-dimensional feasibility problem and an electricvehicle (EV) charging control problem.

A posteriori probabilistic feasibility guarantees for Nash equilibria in uncertain multi-agent games