On the robustness of equilibria in generalized aggregative games

We assess the robustness of equilibria in generalized Nash equilibrium problems in aggregative form subject to linear coupling constraints affected by uncertainty with a possibly unknown probability distribution. Within a data-driven context, we apply the scenario approach paradigm to provide a-post...

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Veröffentlicht in:Proceedings of the IEEE Conference on Decision & Control S. 3725 - 3730
Hauptverfasser: Fabiani, Filippo, Margellos, Kostas, Goulart, Paul J.
Format: Tagungsbericht
Sprache:Englisch
Veröffentlicht: IEEE 14.12.2020
Schlagworte:
Couplings
Games
Nash equilibrium
Probabilistic logic
Probability distribution
Robustness
Uncertainty
ISSN:2576-2370
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Abstract We assess the robustness of equilibria in generalized Nash equilibrium problems in aggregative form subject to linear coupling constraints affected by uncertainty with a possibly unknown probability distribution. Within a data-driven context, we apply the scenario approach paradigm to provide a-posteriori feasibility certificates for the entire set of generalized Nash equilibria of the game. We then show that assessing the violation probability of such a set only requires one to enumerate the constraints that "shape" it. For the class of aggregative games, this results in solving a feasibility problem on each active facet of the feasibility region, for which we propose a semi-decentralized, structure-preserving algorithm.
AbstractList We assess the robustness of equilibria in generalized Nash equilibrium problems in aggregative form subject to linear coupling constraints affected by uncertainty with a possibly unknown probability distribution. Within a data-driven context, we apply the scenario approach paradigm to provide a-posteriori feasibility certificates for the entire set of generalized Nash equilibria of the game. We then show that assessing the violation probability of such a set only requires one to enumerate the constraints that "shape" it. For the class of aggregative games, this results in solving a feasibility problem on each active facet of the feasibility region, for which we propose a semi-decentralized, structure-preserving algorithm.
Author Margellos, Kostas
Goulart, Paul J.
Fabiani, Filippo
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  givenname: Filippo
  surname: Fabiani
  fullname: Fabiani, Filippo
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  organization: University of Oxford,Department of Engineering Science,United Kingdom,OX1 3PJ
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  givenname: Kostas
  surname: Margellos
  fullname: Margellos, Kostas
  email: kostas.margellospaul.goulart@eng.ox.ac.uk
  organization: University of Oxford,Department of Engineering Science,United Kingdom,OX1 3PJ
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  givenname: Paul J.
  surname: Goulart
  fullname: Goulart, Paul J.
  email: paul.goulart@eng.ox.ac.uk
  organization: University of Oxford,Department of Engineering Science,United Kingdom,OX1 3PJ
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Snippet We assess the robustness of equilibria in generalized Nash equilibrium problems in aggregative form subject to linear coupling constraints affected by...
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StartPage 3725
SubjectTerms Couplings
Games
Nash equilibrium
Probabilistic logic
Probability distribution
Robustness
Uncertainty
Title On the robustness of equilibria in generalized aggregative games
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