Optimal Multi-unit Allocation with Costly Verification
81 Pages Posted: 25 Jun 2019 Last revised: 18 Oct 2022
Date Written: June 19, 2019
Abstract
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 check any agent’s value at a cost. We characterize the direct mechanism which maximizes the principal’s net expected payoff. While such a mechanism itself is not obviously strategy-proof, we show that its outcome is easily implementable by an extensive game which has an equilibrium in obviously dominant strategies. 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.
Keywords: mechanism design; costly verification; multiple goods; obviously strategy-proof implementation.
JEL Classification: D82
Suggested Citation: Suggested Citation