ENBIS-17 in Naples

9 – 14 September 2017; Naples (Italy) Abstract submission: 21 November 2016 – 10 May 2017

Solving Kalai-Smorodinski Equilibria Using Gaussian Process Regression

12 September 2017, 12:10 – 12:40


Submitted by
Victor Picheny
Victor Picheny (INRA), Mickael Binois (Chicago Booth School of Business), Abderrahmane Habbal (Universite Cote d'Azur)
Game theory arose from the need to model economic behavior, where multiple decision makers with antagonistic goals is a natural feature. Nowadays it finds a broad range of applications in machine learning and engineering. In this context, the Kalai-Smorodinski (KS) equilibrium is a particularly attractive concept, as it mixes game theory concepts with multi-criteria decision ones (in particular, Pareto-optimality). However, in a derivative-free, expensive, noisy black-box context (e.g. computer experiments), there is no algorithmic solution available to find KS equilibria. Here, we propose a novel Gaussian-process based approach for finding KS equilibria, in the form of a Bayesian optimization algorithm, with sequential sampling decisions based on acquisition functions. Our approach is evaluated on several synthetic game problems with varying number of players and decision space dimensions, including a finite-element model for a Cauchy problem. 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, and illustrate how the KS solution is an attractive alternative to multi-objective optimization.
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