Games of Capacity Manipulation in Hospital-Intern Markets

In this paper, we analyze capacity manipulation games in hospital-intern markets inspired by the real-life entry-level labor markets for young physicians seeking residencies at hospitals. In these markets, where the matching is determined by a centralized clearinghouse called the National Residency Matching Program (NRMP) in the USA, hospitals usually report the number of vacant positions to the NRMP as well as their preferences. We consider a model where preferences of hospitals and interns are common knowledge, and hospitals play a game of reporting their capacities. We characterize the equilibria of the game-form for the two most widely used stable rules: hospital-optimal and intern-optimal stable rules. We show that (i) there may not be a pure strategy equilibrium in general; and (ii) when a pure strategy equilibrium exists other than true-capacities, truthful capacity revelation is weakly Pareto-dominated for hospitals. We also analyze other properties of the set of Nash equilibria. Finally, we present sufficient conditions on preferences to guarantee the existence of pure strategy equilibria.two-sided matching problem, capacity manipulation, Nash equilibrium