The Scope of Sequential Screening with Ex-Post Participation Constraints

71 Pages Posted: 29 Jun 2018

See all articles by Dirk Bergemann

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

Multiple version iconThere are 4 versions of this paper

Date Written: June 13, 2018

Abstract

We study the classic sequential screening problem in the presence of buyers’ ex-post participation constraints. A leading example is the online display advertising market, in which publishers frequently do not use up-front fees and instead use transaction-contingent fees. We establish conditions under which the optimal selling mechanism is static and buyers are not screened with respect to their interim type, or sequential and the buyers are screened with respect to their interim type. In particular, we provide an intuitive necessary and sufficient condition under which the static contract is optimal for general distributions of ex-post values. Further, we completely characterize the optimal sequential contract with binary interim types and continuum of ex-post values when this condition fails. Importantly, the latter contract randomizes the allocation of the low type buyer while giving a deterministic allocation to the high type. We also provide partial results for the case of multiple interim types.

Keywords: Sequential screening, Ex-post participation constraints, Static contract, Sequential 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 (June 13, 2018). Cowles Foundation Discussion Paper No. 2078R2; Columbia Business School Research Paper No. 18-55. Available at SSRN: https://ssrn.com/abstract=3198767 or http://dx.doi.org/10.2139/ssrn.3198767

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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