A variational inequality formulation of a migration model with random data

In this note, we consider a simple model of populations distribution based on utility functions theory. The novelty of our approach is the use of a recent theory of random variational inequalities in refining a previous model by allowing random fluctuations in the data of the problem. We first present the random equilibrium conditions and prove their equivalence to a parametric random variational inequality. Then, we provide a formulation of the problem in a Lebesgue space with a probability measure. Finally, we work out a simple example, which can be solved exactly and allows us to test an approximation procedure.