Optimal Auction Design with Deferred Inspection and Reward

49 Pages Posted: 16 Nov 2020 Last revised: 23 Mar 2022

See all articles by Saeed Alaei

Saeed Alaei

Independent

Alexandre Belloni

Duke University - Fuqua School of Business

Ali Makhdoumi

Fuqua School of Business; Massachusetts Institute of Technology (MIT)

Azarakhsh Malekian

University of Toronto - Rotman School of Management; Massachusetts Institute of Technology (MIT) - Electrical Engineering and Computer Science

Date Written: September 27, 2020

Abstract

Consider a mechanism run by an auctioneer who can use both payment and inspection instruments to incentivize agents. The timeline of the events is as follows. Based on a pre-specified allocation rule and the reported values of agents, the auctioneer allocates the item and secures the reported values as deposits. The auctioneer then inspects the values of agents and, using a pre-specified reward rule, rewards the ones that have reported truthfully. Using techniques from convex analysis and calculus of variation, for any distribution of values, we fully characterize the optimal mechanism for a single agent. Using Border's theorem and duality, we find conditions under which our characterization extends to multiple agents. Interestingly, the optimal allocation function, unlike the classic settings without inspection, is not a thresholding strategy and instead is an increasing and continuous function of the types. We also present an implementation of our optimal auction and show that it achieves a higher revenue than auctions in classic settings without inspection. This is because the inspection enables the auctioneer to charge payments closer to agent's true value without creating incentives for them to deviate to lower types.

Suggested Citation

Alaei, Saeed and Belloni, Alexandre and Makhdoumi, Ali and Malekian, Azarakhsh, Optimal Auction Design with Deferred Inspection and Reward (September 27, 2020). Available at SSRN: https://ssrn.com/abstract=3700525 or http://dx.doi.org/10.2139/ssrn.3700525

Saeed Alaei

Independent ( email )

Alexandre Belloni

Duke University - Fuqua School of Business ( email )

Box 90120
Durham, NC 27708-0120
United States

Ali Makhdoumi (Contact Author)

Fuqua School of Business ( email )

Box 90120
Durham, NC 27708-0120
United States

HOME PAGE: http://https://www.fuqua.duke.edu/faculty/ali-makhdoumi

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

Azarakhsh Malekian

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S 3E6 M5S1S4
Canada

Massachusetts Institute of Technology (MIT) - Electrical Engineering and Computer Science ( email )

77 Massachusetts Avenue
Cambridge, MA 02139-4307
United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
445
Abstract Views
1,772
Rank
123,428
PlumX Metrics