This paper investigates the effect of patient choice on kidney allocation using the following sequential stochastic assignment model. There are n transplant patients to be allocated n kidneys that will arrive sequentially. Each patient and each kidney has its own type, kidney types are random and revealed upon arrival, and the reward from allocating a kidney to a particular patient depends on both their types. Patients may choose to accept or decline any kidney offer. The objective is to determine a kidney allocation policy that maximizes total expected reward subject to the constraint that patients will only accept offers that maximize their own expected reward. A partition policy, in which the space of kidney types is divided into different domains (each corresponding to a different patient type) and in which each kidney is allocated to the patient type corresponding to its domain, is shown to be asymptotically optimal when patients must accept all kidney offers. To reflect patient choice, an incentive compatibility condition is derived to ensure that the offers made by the allocation policy are never declined. This condition is then used to derive a ‘second-best’ partition policy. A numerical example, based on data from the US transplantation system, demonstrates that patient choice may introduce substantial inefficiencies, but the second-best policy recovers all the losses by minimizing the variability in the type of offers expected by each patient. Thus, policy makers should explicitly recognize the effect of patient choice when designing a kidney allocation system.
