Sample average approximation of conditional value-at-risk based variational inequalities

Abstract This paper focuses on a class of variational inequalities (VIs), where the map defining VI is given by component-wise conditional value-at-risk (CVaR) random function. We focus solving using sample average approximation, solutions are estimated with that uses empirical estimates CVaRs. establish two properties for this scheme. First, under continuity and uncertainty taking values in bounded set, we prove asymptotic consistency, establishing almost sure convergence solution problem to true solution. Second, additional assumption functions being Lipschitz, exponential probability distance between an approximate smaller than any constant approaches unity exponentially fast. The decay bound refined case have specific separable form decision variable uncertainty. adapt these results uncertain routing games derive explicit guarantees obtaining CVaR-based Wardrop equilibria procedure. illustrate our theoretical findings approximating modified Sioux Falls network.