Optimal Dynamic Mechanism Design and the Virtual Pivot Mechanism

26 Pages Posted: 10 Mar 2011 Last revised: 14 Feb 2014

Sham Kakade

University of Pennsylvania - Statistics Department

Ilan Lobel

New York University (NYU)

Hamid Nazerzadeh

University of Southern California - Marshall School of Business

Date Written: March 2013

Abstract

We consider the problem of designing optimal mechanisms for settings where agents have dynamic private information. We present the Virtual-Pivot Mechanism, that is optimal in a large class of environments that satisfy a separability condition. The mechanism satisfies a rather strong equilibrium notion (it is periodic ex-post incentive compatible and individually rational). We provide both necessary and sufficient conditions for immediate incentive compatibility for mechanisms that satisfy periodic ex-post incentive compatibility in future periods. The result also yields a strikingly simple mechanism for selling a sequence of items to a single buyer. We also show the allocation rule of the Virtual-Pivot Mechanism has a very simple structure (a Virtual Index) in multi-armed bandit settings. Finally, we show through examples that the relaxation technique we use does not produce optimal dynamic mechanisms in general non-separable environments.

Keywords: optimal mechanism design, dynamic mechanism design, dynamic private information

JEL Classification: D82, C73

Suggested Citation

Kakade, Sham and Lobel, Ilan and Nazerzadeh, Hamid, Optimal Dynamic Mechanism Design and the Virtual Pivot Mechanism (March 2013). Available at SSRN: https://ssrn.com/abstract=1782211 or http://dx.doi.org/10.2139/ssrn.1782211

Sham Kakade

University of Pennsylvania - Statistics Department ( email )

Wharton School
Philadelphia, PA 19104
United States

Ilan Lobel (Contact Author)

New York University (NYU) ( email )

Bobst Library, E-resource Acquisitions
20 Cooper Square 3rd Floor
New York, NY 10003-711
United States

Hamid Nazerzadeh

University of Southern California - Marshall School of Business ( email )

Bridge Memorial Hall
Los Angeles, CA 90089
United States

HOME PAGE: http://www-bcf.usc.edu/~nazerzad/

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