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The B.E. Journal of Theoretical Economics

Editor-in-Chief: Schipper, Burkhard

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1935-1704
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Position Auctions with Budgets: Existence and Uniqueness

Itai Ashlagi
  • 1Harvard Business School, Harvard University,
/ Mark Braverman
  • 2Microsoft Research New England,
/ Avinatan Hassidim
  • 3MIT,
/ Ron Lavi
  • 4Technion – Israel Institute of Technology,
/ Moshe Tennenholtz
  • 5Microsoft Israel R&D Center and Technion – Israel Institute of Technology,
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

About the article

Published Online: 2010-05-14


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

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