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The B.E. Journal of Theoretical Economics

Editor-in-Chief: Schipper, Burkhard

Ed. by Fong, Yuk-fai / Peeters, Ronald / Puzzello , Daniela / Rivas, Javier / Wenzelburger, Jan

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Position Auctions with Budgets: Existence and Uniqueness

Itai Ashlagi / Mark Braverman / Avinatan Hassidim / Ron Lavi / Moshe Tennenholtz
Published Online: 2010-05-14 | DOI: https://doi.org/10.2202/1935-1704.1648

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.

Keywords: position auctions; envy-free allocations; Pareto-efficiency; budget constraints; expost implementation

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Published Online: 2010-05-14

Citation Information: The B.E. Journal of Theoretical Economics, Volume 10, Issue 1, ISSN (Online) 1935-1704, DOI: https://doi.org/10.2202/1935-1704.1648.

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