Vickrey auctions with reserve pricing

DOI: 10.1007/s00199-003-0398-8Economic Theory 23, 493505 (2004)Lawrence M. Ausubel and Peter CramtonDepartment of Economics, University of Maryland, College Park, MD 20742-7211, USA

(e-mail: [email protected]; [email protected])Received: December 31, 2002; revised version: May 5, 2003Summary. We generalize the Vickrey auction to allow for reserve pricing in a

multi-unit auction with interdependent values. In the Vickrey auction with reserve

pricing, the seller determines the quantity to be made available as a function of the

bidders reports of private information, and then efciently allocates this quantity

among the bidders. Truthful bidding is a dominant strategy with private values and

an ex post equilibrium with interdependent values. If the auction is followed by

resale, then truthful bidding remains an equilibrium in the auction-plus-resale game.

In settings with perfect resale, the Vickrey auction with reserve pricing maximizes

seller revenues.Keywords and Phrases: Auctions, Vickrey auctions, Multi-unit auctions, Reserve

price, Resale.JEL Classication Numbers: D44, C78, D82.1 IntroductionA Vickrey auction has the distinct advantage of assigning goods efciently putting

the goods in the hands of those who value them most. However, one critique of

a Vickrey auction is that it may yield low revenues for the seller. Indeed, Vickrey[star] The authors gratefully acknowledge the generous support of National Science Foundation Grants

SES-97-31025, SES-01-12906 and IIS-02-05489. We appreciate valuable comments from Ilya Segal.

Special thanks go to Mordecai Kurz, who served as Larrys dissertation advisor and who introduced

both authors to the economics profession back at IMSSS at Stanford. Congratulations and best wishes

are extended to Mordecai and his family on the happy occasion of the publication of Assets, Beliefs,

and Equilibria in Economic Dynamics: Essays in Honor of Mordecai Kurz, in which this article also

appears.Correspondence to: L.M. AusubelVickrey auctions with reserve pricing[star]494 L.M. Ausubel and P. Cramtonexpressed this concern in his seminal article (Vickrey, 1961). When competition

is weak and the bidders are asymmetric, revenues from a Vickrey auction may

be small. A vivid example was the 1990 New Zealand sale of spectrum licenses

by second-price auction. In one case, the winner bid $100,000, but paid only $6;

in another, the winner bid $7,000,000, but paid only $5,000 (McMillan, 1994).

Reserve pricing is a simple and effective device to avoid such disasters. The seller

may charge the reserve price or reduce the quantity sold...