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.

Automated summary

In this paper, a stochastic Generalized Nash Equilibrium model is proposed to describe the competition among hospitals with first aid departments in a disaster scenario. Each hospital needs to solve a two-stage stochastic optimization problem to determine the equilibrium hospitalization flows to dispatch to other hospitals. The model defines the Generalized Nash Equilibria and focuses on the Variational Equilibria obtained from a variational inequality problem. A numerical example is presented to validate the model's effectiveness.