Random Variational Inequalities with Applications to Equilibrium Problems under Uncertainty

In this contribution we introduce to the topic of Random Variational Inequalities (RVI) and present some of our recent results in this field. We show how the theory of monotone RVI, where random variables occur both in the operator and the constraints set, can be applied to model nonlinear equilibrium problems under uncertainty arising from economics and operations research, including migration and transportation science. In particular we treat Wardrop equilibria in traffic networks. We describe an approximation procedure for the statistical quantities connected to the equilibrium solution and illustrate this procedure by means of some small sized numerical examples.