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On the Continuous Equilibria of Affiliated-Value, All-Pay Auctions with Private Budget Constraints

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  • Maciej H. Kotowski

    ()
    (Harvard Kennedy School)

  • Fei Li

    ()
    (Department of Economics, University of Pennsylvania)

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    Abstract

    We consider all-pay auctions in the presence of interdependent, affiliated valuations and private budget constraints. For the sealed-bid, all-pay auction we characterize a symmetric equilibrium in continuous strategies for the case of N bidders and we investigate its properties. Budget constraints encourage more aggressive bidding among participants with large endowments and intermediate valuations. We extend our results to the war of attrition where we show that budget constraints lead to a uniform amplification of equilibrium bids among bidders with sufficient endownments. An example shows that with both interdependent valuations and private budget constraints, a revenue ranking between the two mechanisms is generally not possible.

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    Bibliographic Info

    Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 12-019.

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    Length: 44 pages
    Date of creation: 23 Apr 2012
    Date of revision:
    Handle: RePEc:pen:papers:12-019

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    Keywords: All-Pay Auction; War of Attrition; Budget Constraints; Common Values; Private Values; Affiliation; Contests;

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    1. Baye, Michael R & Kovenock, Dan & de Vries, Casper G, 1993. "Rigging the Lobbying Process: An Application of the All-Pay Auction," American Economic Review, American Economic Association, vol. 83(1), pages 289-94, March.
    2. Eric Maskin & John Riley, 2003. "Uniqueness of Equilibrium in Sealed High-Bid Auctions," Economics Working Papers 0031, Institute for Advanced Study, School of Social Science.
    3. Che, Yeon-Koo & Gale, Ian, 2006. "Revenue comparisons for auctions when bidders have arbitrary types," Theoretical Economics, Econometric Society, vol. 1(1), pages 95-118, March.
    4. Lebrun, Bernard, 1999. "First Price Auctions in the Asymmetric N Bidder Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(1), pages 125-42, February.
    5. Che, Yeon-Koo & Gale, Ian, 1998. "Standard Auctions with Financially Constrained Bidders," Review of Economic Studies, Wiley Blackwell, vol. 65(1), pages 1-21, January.
    6. Luciano I. de Castro, 2007. "Affiliation, equilibrium existence and the revenue ranking of auctions," Economics Working Papers we074622, Universidad Carlos III, Departamento de Economía.
    7. Patrick Bajari & Ali Hortacsu, 2003. "Are Structural Estimates of Auction Models Reasonable? Evidence from Experimental Data," Working Papers 03002, Stanford University, Department of Economics.
    8. Krishna, Vijay & Morgan, John, 1997. "An Analysis of the War of Attrition and the All-Pay Auction," Journal of Economic Theory, Elsevier, vol. 72(2), pages 343-362, February.
    9. Leininger, Wolfgang, 1991. "Patent competition, rent dissipation, and the persistence of monopoly: The role of research budgets," Journal of Economic Theory, Elsevier, vol. 53(1), pages 146-172, February.
    10. Fang, Hanming & Parreiras, Sergio O., 2003. "On the failure of the linkage principle with financially constrained bidders," Journal of Economic Theory, Elsevier, vol. 110(2), pages 374-392, June.
    11. Athey, Susan & Haile, Philip A., 2007. "Nonparametric Approaches to Auctions," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 60 Elsevier.
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