  We study stochastic Nash equilibrium problems subject to heterogeneous
uncertainty on the cost functions of the individual agents. In our setting, we
assume no prior knowledge of the underlying probability distributions of the
uncertain variables. To account for this lack of knowledge, we consider an
ambiguity set around the empirical probability distribution under the
Wasserstein metric. We then show that, under mild assumptions, finite-sample
guarantees on the probability that any resulting distributionally robust Nash
equilibrium is also robust with respect to the true probability distributions
with high confidence can be obtained. Furthermore, by recasting the game as a
distributionally robust variational inequality, we establish asymptotic
convergence of the set of data-driven distributionally robust equilibria to the
solution set of the original game. Finally, we recast the distributionally
robust Nash game as a finite-dimensional Nash equilibrium problem. We
illustrate the proposed distributionally robust reformulation via numerical
experiments of stochastic Nash-Cournot games.
