The Scope of Sequential Screening with Ex-Post Participation Constraints

53 Pages Posted: 22 Feb 2017  

Dirk Bergemann

Yale University - Cowles Foundation - Department of Economics; Yale University - Cowles Foundation

Francisco Castro

Columbia Business School - Decision Risk and Operations

Gabriel Y. Weintraub

Stanford Graduate School of Business, Stanford University; Columbia University - Columbia Business School - Decision Risk and Operations

Date Written: February 18, 2017

Abstract

We study the classic sequential screening problem under ex-post participation constraints. Thus the seller is required to satisfy buyers’ ex-post participation constraints. A leading example is the online display advertising market, in which publishers frequently cannot use up-front fees and instead use transaction-contingent fees.

We establish when the optimal selling mechanism is static (buyers are not screened) or dynamic (buyers are screened), and obtain a full characterization of such contracts. We begin by analyzing our model within the leading case of exponential distributions with two types. We provide a necessary and sufficient condition for the optimality of the static contract. If the means of the two types are sufficiently close, then no screening is optimal. If they are sufficiently apart, then a dynamic contract becomes optimal. Importantly, the latter contract randomizes the low type buyer while giving a deterministic allocation to the high type. It also makes the low type worse-off and the high type better-off compared to the contract the seller would offer if he knew the buyer’s type. Our main result establishes a necessary and sufficient condition under which the static contract is optimal for general distributions. We show that when this condition fails, a dynamic contract that randomizes the low type buyer is optimal.

Keywords: Sequential Screening, Ex-Post Participation Constraints, Static Contract, Dynamic Contract

JEL Classification: C72, D82, D83

Suggested Citation

Bergemann, Dirk and Castro, Francisco and Weintraub, Gabriel Y., The Scope of Sequential Screening with Ex-Post Participation Constraints (February 18, 2017). Cowles Foundation Discussion Paper No. 2078; Columbia Business School Research Paper No. 17-29. Available at SSRN: https://ssrn.com/abstract=2921459

Dirk Bergemann (Contact Author)

Yale University - Cowles Foundation - Department of Economics ( email )

28 Hillhouse Ave
New Haven, CT 06520-8268
United States
203-432-3592 (Phone)
203-432-2128 (Fax)

HOME PAGE: http://www.econ.yale.edu/~dirk/

Yale University - Cowles Foundation

Box 208281
New Haven, CT 06520-8281
United States

Francisco Castro

Columbia Business School - Decision Risk and Operations ( email )

New York, NY
United States

Gabriel Y. Weintraub

Stanford Graduate School of Business, Stanford University ( email )

Stanford, CA 94305
United States

Columbia University - Columbia Business School - Decision Risk and Operations ( email )

New York, NY
United States

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