  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.
