Ascending Price Vickrey Auctions for General Valuations

CORE Discussion Paper No. 2005/52

38 Pages Posted: 30 Jun 2006

See all articles by Debasis Mishra

Debasis Mishra

Indian Statistical Institute, New Delhi - Delhi Centre

David C. Parkes

Harvard University - Division of Engineering and Applied Sciences

Date Written: August 2005

Abstract

Ascending price auctions typically involve a single price path with buyers paying their final bid price. Using this traditional definition, no ascending price auction can achieve the Vickrey-Clarke-Groves (VCG) outcome for general private valuations in the combinatorial auction setting. We relax this definition by allowing discounts to buyers from the final price of the auction (or alternatively, calculating the discounts dynamically during the auction) while still maintaining a single price path. Using a notion called universal competitive equilibrium prices, shown to be necessary and sufficient to achieve the VCG outcome using ascending price auctions, we define a broad class of ascending price combinatorial auctions in which truthful bidding by buyers is an ex post Nash equilibrium. Any auction in this class achieves the VCG outcome and ex post efficiency for general valuations. We define two specific auctions in this class by generalizing two known auctions in the literature [11, 24].

Keywords: combinatorial auctions, multi-item auctions, primal-dual algorithm, universal competitive equilibrium, Vickrey auctions

JEL Classification: D44, D50, C62

Suggested Citation

Mishra, Debasis and Parkes, David C., Ascending Price Vickrey Auctions for General Valuations (August 2005). CORE Discussion Paper No. 2005/52, Available at SSRN: https://ssrn.com/abstract=912241 or http://dx.doi.org/10.2139/ssrn.912241

Debasis Mishra (Contact Author)

Indian Statistical Institute, New Delhi - Delhi Centre ( email )

7 S .J. S.
Sansanwal Marg
New Delhi, 110016
India

David C. Parkes

Harvard University - Division of Engineering and Applied Sciences ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States

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