We consider a multi-agent noncooperative game with agents’ objective functions being affected by uncertainty. Following a data driven paradigm, we represent uncertainty by means of scenarios and seek a robust Nash equilibrium solution. We treat the Nash equilibrium computation problem within the realm of probably approximately correct (PAC) learning. Building upon recent developments in scenario-based optimization, we accompany the computed Nash equilibrium with a priori and a posteriori probabilistic robustness certificates, providing confidence that the computed equilibrium remains unaffected (in probabilistic terms) when a new uncertainty realization is encountered. For a wide class of games, we also show that the computation of the so called compression set — which is at the core of scenario-based optimization — can be directly obtained as a byproduct of the proposed methodology. We demonstrate the efficacy of our approach on an electric vehicle charging control problem.
Probably approximately correct Nash equilibrium learning
07.10.2020
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
DDC: | 629 |
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