A Two-Stage Variational Inequality Formulation for a Game Theory Network Model for Hospitalization in Critic Scenarios

In this paper, we introduce the theoretical structure of a stochastic Generalized Nash Equilibrium model describing the competition among hospitals with first aid departments for the hospitalization in a disaster scenario. Each hospital with a first aid department has to solve a two-stage stochastic optimization problem, one before the declaration of the disaster scenario and one after the disaster advent, to determine the equilibrium hospitalization flows to dispatch to the other hospitals with first aid and/or to hospitals without emergency rooms in the network. We define the Generalized Nash Equilibria of the model and, particularly, we consider the Variational Equilibria which is obtained as the solution to a variational inequality problem. Finally, we present a basic numerical example to validate the effectiveness of the model.