Optimal provision-after-wait in healthcare. Available at http: //www.cs.princeton.edu/˜mbraverm/pmwiki/index.php?n=Research.AllPapers

We investigate computational and mechanism design aspects of optimal scarce resource allocation, where the primary rationing mechanism is through waiting times. Specifically we consider the problem of allocating medical treatments to a population of patients. Each patient has demand for exactly one unit of treatment, and can choose to be treated in one of k hospitals, H1,...,Hk. Different hospitals have different costs, which are fully paid by a third party —the “payer” — and do not accrue to the patients. The payer has a fixed budget B and can only cover a limited number of treatments in the more expensive hospitals. Access to over-demanded hospitals is rationed through waiting times: each hospital Hi will have waiting time wi. In equilibrium, each patient will choose his most preferred hospital given his intrinsic preferences and the waiting times. The payer thus computes the waiting times and the number of treatments authorized for each hospital, so that in equilibrium the budget constraint is satisfied and the social welfare is maximized. We show that even if the patients ’ preferences are known to the payer, the task of optimizing social welfare in equilibrium subject to the budget constraint is NP-hard. We also show that, if the number of hospitals is small and the budget constraint can be relaxed from B to (1 + )B for an arbitrarily small constant , then the original optimum under budget B can be achieved efficiently. Next, we study the endogenous emergence of waiting time from the dynamics between hospitals an