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Optimal Stopping with Private Information

34 Pages Posted: 10 Jul 2013 Last revised: 8 May 2014

Thomas Kruse

Université d'Évry - Departement de Mathematiques

Philipp Strack

University of California, Berkeley - Department of Economics

Date Written: May 6, 2014

Abstract

Many economic situations are modeled as stopping problems. Examples include job search, timing of market entry decisions, irreversible investment or the pricing of American options. This paper analyzes optimal stopping as a mechanism design problem with transfers. We show that a under a dynamic single crossing condition a stopping rule can be implemented by a transfer that only depends on the realized stopping decision if and only if it is a cut-off rule. We characterize the transfer implementing a given stopping rule using a novel technique based on constrained stochastic processes.

As an application we prove that in any Markovian optimal stopping problem there exists a welfare maximizing mechanism that does not require any communication. We discuss revenue maximization for separable processes.

Keywords: Dynamic Mechanism Design, Optimal Stopping, Dynamic Implementability, Posted-Price Mechanism

JEL Classification: D82, C62

Suggested Citation

Kruse, Thomas and Strack, Philipp, Optimal Stopping with Private Information (May 6, 2014). Available at SSRN: https://ssrn.com/abstract=2291937 or http://dx.doi.org/10.2139/ssrn.2291937

Thomas Kruse

Université d'Évry - Departement de Mathematiques ( email )

Rue du Pere Jarlan
Evry, 91025
France

Philipp Strack (Contact Author)

University of California, Berkeley - Department of Economics ( email )

549 Evans Hall #3880
Berkeley, CA 94720-3880
United States

HOME PAGE: http://philippstrack.com

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