Application of Game Theory Analysis in Epidemiology and Service Management

We present two game theoretic models on resource allocation in epidemic control and waiting time competition in service management. The first model considers the drug allocation problem when facing the outbreak of an international influenza pandemic. The drugs are for prophylactic use. Since drug stockpiles are presently scattered in different countries, the outbreak of an epidemic gives rise to a game in which each country must make decisions about how best to allocate its own stockpile in order to protect its population. We develop a two-period multivariate Reed-Frost model to represent the spread of the epidemic within and across countries at its onset. We show that for small probability of between-country infections, the underlying game is supermodular and that a unique Pareto optimal Nash equilibrium exists. Further, we identify sufficient conditions under which the optimal solution of a central planner constitutes a Pareto improvement over the decentralized equilibrium. The second model investigates the impact of reference effect on firms' waiting time competition. We consider two firms (modeled as M/M/1 queueing facilities) announcing the expected waiting times to attract customers. Customers' joining decisions depend not only on the announced waiting times, but also on the reference effect, as demonstrated by the psychology literature. Reference effect, modeled in the spirit of prospect theory, is a "kinked" function of the gap between customers' expectation and perception of the waiting time, where the expectation is formed by both firms'announcements. We prove the existence of a unique (Pareto optimal) Nash equilibrium in the presence of reference effect. We show that comparing to the no reference effect case, the equilibrium waiting times are shorter and firms tend to announce a same waiting time.