A Bayesian optimization approach to find Nash equilibria

Victor Picheny (), Mickael Binois () and Abderrahmane Habbal ()
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Victor Picheny: Université de Toulouse, INRA
Mickael Binois: The University of Chicago Booth School of Business
Abderrahmane Habbal: Université Côte d’Azur

Journal of Global Optimization, 2019, vol. 73, issue 1, No 7, 192 pages

Abstract: Abstract Game theory finds nowadays a broad range of applications in engineering and machine learning. However, in a derivative-free, expensive black-box context, very few algorithmic solutions are available to find game equilibria. Here, we propose a novel Gaussian-process based approach for solving games in this context. We follow a classical Bayesian optimization framework, with sequential sampling decisions based on acquisition functions. Two strategies are proposed, based either on the probability of achieving equilibrium or on the stepwise uncertainty reduction paradigm. Practical and numerical aspects are discussed in order to enhance the scalability and reduce computation time. Our approach is evaluated on several synthetic game problems with varying number of players and decision space dimensions. We show that equilibria can be found reliably for a fraction of the cost (in terms of black-box evaluations) compared to classical, derivative-based algorithms. The method is available in the R package GPGame available on CRAN at https://cran.r-project.org/package=GPGame .

Keywords: Game theory; Gaussian processes; Stepwise uncertainty reduction (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10898-018-0688-0

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