Optimal Multi-unit Allocation with Costly Verification

81 Pages Posted: 25 Jun 2019 Last revised: 18 Oct 2022

See all articles by Geoffrey A. Chua

Geoffrey A. Chua

Nanyang Technological University

Gaoji Hu

Shanghai University of Finance and Economics - School of Economics

Fang Liu

Durham University Business School

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

Chua, Geoffrey A. and Hu, Gaoji and Liu, Fang, Optimal Multi-unit Allocation with Costly Verification (June 19, 2019). Available at SSRN: https://ssrn.com/abstract=3407031 or http://dx.doi.org/10.2139/ssrn.3407031

Geoffrey A. Chua

Nanyang Technological University ( email )

50 Nanyang Avenue
S3-B2A-04
Singapore, Singapore 639798
Singapore

Gaoji Hu (Contact Author)

Shanghai University of Finance and Economics - School of Economics ( email )

777 Guoding Road
Shanghai, 200433
China

Fang Liu

Durham University Business School ( email )

Mill Hill Lane
Durham, DH1 3LB
United Kingdom

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