Probabilistic sensitivity of Nash equilibria in multi-agent games: a wait-and-judge approach
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Motivated by electric vehicle charging control problems, we consider multi-agent noncooperative games where, following a data driven paradigm, unmodeled externalities acting on the players' objective functions are represented by means of scenarios. Building upon recent developments in scenario-based optimization, based on the evaluation of the computed solution, we accompany the Nash equilibria of the uncertain game with an a posteriori probabilistic robustness certificate, providing confidence on the probability that the computed solution remains unaffected when a new uncertainty realisation is encountered. 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.
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