Optimal Allocation with Costly Verification

A principal (dean) has an object (job slot) to allocate to one of I agents (departments). Each agent has a strictly positive value for receiving the object. Each agent also has private information which determines the value to the principal of giving the object to him. There are no monetary transfers but the principal can check the value associated with any individual at a cost which may vary across individuals. We characterize the class of optimal Bayesian mechanisms, that is, mechanisms which maximize the expected value to the principal from his assignment of the good minus the costs of checking values. One particularly simple mechanism in this class, which we call the favored–agent mechanism, specifies a threshold value v∗ and a favored agent i∗. If all agents other than i∗ report values below v∗, then i∗ receives the good and no one is checked. Otherwise, whoever reports the highest value is checked with probability 1 and receives the good iff her report is confirmed. We show that all optimal mechanisms are essentially randomizations over optimal favored–agent mechanisms.