Competition for Medical Supplies Under Stochastic Demand in the Covid-19 Pandemic: A Generalized Nash Equilibrium Framework

The Covid-19 pandemic has negatively impacted virtually all economic and social activities across the globe. Presently, since there is still no vaccine and no curative treatments for this disease, medical supplies in the form of Personal Protective Equipment and ventilators are sorely needed for healthcare workers and certain patients, respectively. The fact that this healthcare disaster is not limited in time and space has resulted in intense global competition for medical supplies. In this paper, we construct the first Generalized Nash Equilibrium model with stochastic demands to model competition among organizations at demand points for medical supplies. The model includes multiple supply points and multiple demand points, along with prices of the medical items and generalized costs associated with transportation. The theoretical constructs are provided and a Variational Equilibrium utilized to enable alternative variational inequality formulations. A qualitative analysis is presented and an algorithm proposed, along with convergence results. Illustrative examples are detailed as well as numerical examples that are solved with the implemented algorithm. The results reveal the impacts of the addition of supply points as well as of demand points on the medical item product flows. The formalism may be adapted to multiple medical items both in the near term and in the longer term (such as for vaccines).