Countering Value Uncertainty via Refunds: A Mechanism Design Approach

30 Pages Posted: 25 Sep 2023

See all articles by Saeed Alaei

Saeed Alaei

Independent

Shuchi Chawla

University of Texas at Austin - Department of Computer Science

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 4, 2023

Abstract

We consider a mechanism design setting with a single item and a single buyer who is uncertain about the value of the item. Both the buyer and the seller have a common model for the buyer's value, but the buyer discovers her true value only upon receiving the item. We show that mechanisms in this setting can be interpreted as randomized refund mechanisms, which allocate the item at some price and then offer a (partial and/or randomized) refund to the buyer in exchange for the item if the buyer is unsatisfied with her purchase. Motivated by their practical importance, we study the design of optimal deterministic mechanisms in this setting. We first characterize optimal mechanisms as virtual value maximizers for both continuous and discrete type settings. We then use this characterization, along with tools like regularity and duality, to develop efficient algorithms for finding optimal and near-optimal deterministic mechanisms.

Keywords: Return policies, Deterministic mechanism design, Online retailers, Approximate optimality

Suggested Citation

Alaei, Saeed and Chawla, Shuchi and Makhdoumi, Ali and Malekian, Azarakhsh, Countering Value Uncertainty via Refunds: A Mechanism Design Approach (September 4, 2023). Available at SSRN: https://ssrn.com/abstract=4561235 or http://dx.doi.org/10.2139/ssrn.4561235

Saeed Alaei

Independent ( email )

Shuchi Chawla

University of Texas at Austin - Department of Computer Science ( email )

2317 Speedway, Stop D9500
Austin, TX
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

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