Distributionally Robust Stochastic Variational Inequalities

We propose a formulation of the distributionally robust variational inequality (DRVI) to deal with uncertainties of distributions of the involved random variables in variational inequalities. Examples of the DRVI are provided, including the optimality conditions for distributionally robust optimization and distributionally robust games (DRG). The existence of solutions and monotonicity of the DRVI are discussed. Moreover, we propose a sample average approximation (SAA) approach to the DRVI and study its convergence properties. Numerical examples of DRG are presented to illustrate solutions of the DRVI and convergence properties of the SAA approach.