Probabilistic sensitivity of Nash equilibria in multi-agent games: a wait-and-judge approach

Motivated by electric vehicle charging control problems, we consider multi-agent noncooperative games where, following a data driven paradigm, unmodelled externalities acting on the players' objective functions are represented by means of scenarios. Overcoming the nondifferentiability characterizing such a setup, we retrieve a Nash equilibrium in a decentralised manner. Then, building upon recent developments in scenario-based optimization, we accompany the given solution with an a posteriori probabilistic robustness certificate, providing confidence that the computed equilibrium remains unaffected by an "unseen" uncertainty realisation. The latter constitutes, to the best of our knowledge, the first application of the so-called scenario approach to multi-agent Nash equilibrium problems. The efficacy of our approach is demonstrated in simulation for the charging coordination of an electric vehicle fleet.