Optimal Multi-unit Allocation with Costly Verification

A principal has n homogeneous objects to allocate to I > n agents. The principal can allocate at most one good to an agent and each agent values the good. Agents have private information about the principal's payoff of allocating the goods. There are no monetary transfers but the principal can costly check any agent's value. We characterize the mechanism which maximizes the principal's net expected payoff. Such an optimal mechanism is a hybrid between two extremes. One extreme allocates the goods efficiently, i.e., to the $n$ agents who have the highest values, which requires agents being checked and leads to very high checking cost; the other incurs no checking cost by allocating without learning agents' value, which results in very large allocation inefficiency. The optimal mechanism balances the benefit of efficiency and the cost of checking. Moreover, it is easy to implement. We also compare the optimal mechanism with an alternative mechanism that allocates the goods one by one, where the single-good optimal mechanism is used in each step. The optimal mechanism dominates such an alternative in a particular way: Under any value profile, the two mechanisms allocate the goods to the same set of agents, but the optimal mechanism checks agents less frequently