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Position Auctions with Budgets: Existence and Uniqueness

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Author Info

  • Ashlagi Itai

    ()
    (Harvard Business School, Harvard University)

  • Braverman Mark

    ()
    (Microsoft Research New England)

  • Hassidim Avinatan

    ()
    (MIT)

  • Lavi Ron

    ()
    (Technion – Israel Institute of Technology)

  • Tennenholtz Moshe

    ()
    (Microsoft Israel R&D Center and Technion – Israel Institute of Technology)

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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.

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    Bibliographic Info

    Article provided by De Gruyter in its journal The B.E. Journal of Theoretical Economics.

    Volume (Year): 10 (2010)
    Issue (Month): 1 (May)
    Pages: 1-32

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    Handle: RePEc:bpj:bejtec:v:10:y:2010:i:1:n:20

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    Cited by:
    1. Rica Gonen & Anat Lerner, 2013. "The Incompatibility of Pareto Optimality and Dominant-Strategy Incentive Compatibility in Sufficiently-Anonymous Budget-Constrained Quasilinear Settings," Games, MDPI, Open Access Journal, vol. 4(4), pages 690-710, November.
    2. Lavi, Ron & May, Marina, 2012. "A note on the incompatibility of strategy-proofness and Pareto-optimality in quasi-linear settings with public budgets," Economics Letters, Elsevier, vol. 115(1), pages 100-103.
    3. Dobzinski, Shahar & Lavi, Ron & Nisan, Noam, 2012. "Multi-unit auctions with budget limits," Games and Economic Behavior, Elsevier, vol. 74(2), pages 486-503.
    4. Hafalir, Isa E. & Ravi, R. & Sayedi, Amin, 2012. "A near Pareto optimal auction with budget constraints," Games and Economic Behavior, Elsevier, vol. 74(2), pages 699-708.

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