We investigate computational and mechanism design aspects of scarce resource allocation, where the primary rationing mechanism is through waiting times. Specifically we consider allocating medical treatments to a population of patients. Each patient needs exactly one treatment, and can choose from @math hospitals. Hospitals have different costs, which are fully paid by a third party ---the "payer". The payer has a fixed budget @math , and each hospital will have its own waiting time. At equilibrium, each patient will choose his most preferred hospital given his intrinsic preferences and the waiting times. The payer thus computes the waiting times so that at equilibrium the budget constraint is satisfied and the social welfare is maximized. We first show that the optimization problem is NP-hard, yet if the budget can be relaxed to @math for an arbitrarily small @math , then the optimum under budget @math can be approximated efficiently. Next, we study the endogenous emergence of waiting time from the dynamics between hospitals and patients, and show that there is no need for the payer to explicitly enforce the optimal waiting times. Under certain conditions, all he need is to enforce the amount of money he wants to pay to each hospital. The dynamics will always converge to the desired waiting times in finite time. We then go beyond equilibrium solutions and investigate the optimization problem over a much larger class of mechanisms containing the equilibrium ones as special cases. With two hospitals, we show that under a natural assumption on the patients' preference profiles, optimal welfare is in fact attained by the randomized assignment mechanism, which allocates patients to hospitals at random subject to the budget constraint, but avoids waiting times. Finally, we discuss potential policy implications of our results, as well as follow-up directions and open problems.
The role of waiting time can be studied either from the supply side, namely, how waiting times interact with the hospitals' incentives, or from the demand side, namely, how they interact with the patients' incentives. In @cite_1 the authors give a thorough analysis of existing policies on reducing waiting times by affecting the incentives of either side. Our model focuses on the demand side, and below we discuss some other works that also focus on this side.
@cite_1
2004972267
This paper compares policies to tackle excessive waiting times for elective surgery in 12 OECD countries. It is found that waiting times may be reduced by acting on the supply of or on the demand for surgery (or both). On the supply side, evidence suggests that both capacity and financial incentives towards productivity can play an important role. On the demand side, inducing a raising of clinical thresholds may reduce waiting times but may also provoke tension between clinicians and policy makers. Preliminary evidence also suggests that an increase in private health insurance coverage may reduce waiting times.