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

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          Abstract

          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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          Games with Incomplete Information Played by “Bayesian” Players, I–III Part I. The Basic Model

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            The Scenario Approach to Robust Control Design

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              Cyber–Physical Systems: A Perspective at the Centennial

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                Author and article information

                Journal
                25 March 2019
                Article
                1903.10387
                5dbb03bb-6ebb-4274-be53-dae884d57120

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                00
                math.OC cs.GT cs.SY

                Theoretical computer science,Numerical methods,Performance, Systems & Control

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