Mechanism Design with Costly Verification and Limited Punishments

A principal allocates an object among a finite number of agents, each of whom values the object. Each agent has access to private information about the principal's payoff if he receives the object. There are no monetary transfers. The object is allocated based on the agents' reports. The principal can inspect agents' reports at a cost and punish them, but punishments are sufficiently limited because verification is imperfect or information arrives only after the object has been allocated for a set period of time. If the number of agents is small, a threshold exists such that all agents whose values are below the threshold are pooled and an optimal allocation rule is efficient at the top of value distributions. If the number of agents is large, an optimal allocation rule also involves pooling at the top. If the number of agents is sufficiently large, the pooling areas at the bottom and the top meet and an optimal mechanism can be implemented via a shortlisting procedure. The fact that optimal mechanisms depend on the number of agents implies that small and large organizations should behave differently