A variational inequality model of the spatial price network problem with uncertain data

We consider the multicriteria spatial price network equilibrium model in which consumers are allowed to weight both the transportation cost and the transportation time associated with the shipment of a given commodity. In particular, we assume that weights are not deterministic but subject to random fluctuations. Therefore, we formulate the problem as a random variational inequality and prove that under natural assumptions the associated random operator satisfies a uniform monotonicity property. The subsequent analysis is carried out in the framework of the theory of random variational inequalities.