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Position Auctions with Budgets: Existence and Uniqueness

Author(s)
Ashlagi, Itai; Braverman, Mark; Hassidim, Avinatan; Lavi, Ron; Tennenholtz, Moshe
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Abstract
We design a Generalized Position Auction for players with private values and private budget constraints. Our mechanism is a careful modification of the Generalized English Auction of Edelman, Ostrovsky and Schwarz (2007). By enabling multiple price trajectories that ascent concurrently we are able to retrieve all the desired properties of the Generalized English Auction, that was not originally designed for players with budgets. In particular, the ex-post equilibrium outcome of our auction is Pareto-efficient and envy-free. Moreover, we show that any other position auction that satisfies these properties and does not make positive transfers must obtain in ex-post equilibrium the same outcome of our mechanism, for every tuple of distinct types. This uniqueness result holds even if the players' values are fixed and known to the seller, and only the budgets are private.
Date issued
2010-05
URI
http://hdl.handle.net/1721.1/64459
Department
Sloan School of Management; W. M. Keck Foundation Center for Extreme Quantum Information Theory
Journal
B E Journal of Theoretical Economics
Publisher
Berkeley Electronic Press
Citation
Ashlagi, Itai; Braverman, Mark; Hassidim, Avinatan; Lavi, Ron; and Tennenholtz, Moshe (2010) "Position Auctions with Budgets: Existence and Uniqueness," The B.E. Journal of Theoretical Economics: Vol. 10 : Iss. 1 (Advances), Article 20. Copyright ©2010 Berkeley Electronic Press
Version: Final published version
ISSN
1935-1704

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