Progressive Participation

49 Pages Posted: 15 Aug 2019

See all articles by Dirk Bergemann

Dirk Bergemann

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

Philipp Strack

Yale, Department of Economics

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Date Written: August 14, 2019

Abstract

A single seller faces a sequence of buyers with unit demand. The buyers are forward-looking and long-lived but vanish (and are replaced) at a constant rate. The arrival time and the valuation is private information of each buyer and unobservable to the seller. Any incentive-compatible mechanism has to induce truth-telling about the arrival time and the evolution of the valuation.

We derive the optimal stationary mechanism, characterize its qualitative structure and derive a closed-form solution. As the arrival time is private information, the agent can choose the time at which he reports his arrival. The truth-telling constraint regarding the arrival time can be represented as an optimal stopping problem. The stopping time determines the time at which the agent decides to participate in the mechanism. The resulting value function of each agent can not be too convex and has to be continuously diļ¬€erentiable everywhere, reflecting the option value of delaying participation. The optimal mechanism thus induces progressive participation by each agent: he participates either immediately or at a future random time.

Keywords: Dynamic Mechanism Design, Observable Arrival, Unobservable Arrival, Repeated Sales, Interim Incentive Constraints, Interim Participation Constraints, Stopping Problem, Option Value, Progressive Participation

JEL Classification: D44, D82, D83

Suggested Citation

Bergemann, Dirk and Strack, Philipp, Progressive Participation (August 14, 2019). Cowles Foundation Discussion Paper No. 2189, Available at SSRN: https://ssrn.com/abstract=3437559 or http://dx.doi.org/10.2139/ssrn.3437559

Dirk Bergemann

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

28 Hillhouse Ave
New Haven, CT 06520-8268
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203-432-3592 (Phone)
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HOME PAGE: http://www.econ.yale.edu/~dirk/

Yale University - Cowles Foundation

Box 208281
New Haven, CT 06520-8281
United States

Philipp Strack (Contact Author)

Yale, Department of Economics ( email )

28 Hillhouse Ave
New Haven, CT 06520-8268
United States

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