  In this paper a distribution-free methodology is presented for providing
robustness guarantees for Nash equilibria (NE) of multi-agent games. Leveraging
recent a posteriori developments of the so called scenario approach (Campi et
al., 2018), we provide probabilistic guarantees for feasibility problems with
polytopic constraints. This result is then used in the context of multi-agent
games, allowing to provide robustness certificates for constraint violation of
any NE of a given game. Our guarantees can be used alongside any NE seeking
algorithm that returns some equilibrium solution. Finally, by exploiting the
structure of our problem, we circumvent the need of employing computationally
prohibitive algorithms to find an irreducible support subsample, a concept at
the core of the scenario approach. Our theoretical results are accompanied by
simulation studies that investigate the robustness of the solutions of two
different problems, namely, a 2-dimensional feasibility problem and an electric
vehicle (EV) charging control problem.
