A Bayesian optimization approach to find Nash equilibria - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Journal of Global Optimization Year : 2019

A Bayesian optimization approach to find Nash equilibria


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 .
Fichier principal
Vignette du fichier
jogo-nash.pdf (689.96 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-01944524 , version 1 (04-12-2018)



Victor Picheny, Mickaël Binois, Abderrahmane Habbal. A Bayesian optimization approach to find Nash equilibria. Journal of Global Optimization, 2019, 73 (1), pp.171 - 192. ⟨10.1007/s10898-018-0688-0⟩. ⟨hal-01944524⟩
681 View
984 Download



Gmail Mastodon Facebook X LinkedIn More