IDEAS home Printed from
   My bibliography  Save this paper

The all-pay auction with non-monotonic payoff


  • Subhashish Modak Chowdhury

    (University of East Anglia)


We analyze an endogenous prize all-pay auction under complete information where it is possible that none of the bidders wins and the winning payoff becomes non-monotonic in own bid. We derive the conditions for the existence of pure strategy equilibria and fully characterize the unique mixed strategy equilibrium when pure strategy equilibria do not exist. The high-valuation bidder places two distinct mass points in his equilibrium mixed strategy and the equilibrium support of the low-valuation bidder is not continuous. Under common valuation, in the equilibrium mixed strategy both bidders place mass points at the same point of the support. Possible applications are discussed.

Suggested Citation

  • Subhashish Modak Chowdhury, 2009. "The all-pay auction with non-monotonic payoff," Working Paper series, University of East Anglia, Centre for Behavioural and Experimental Social Science (CBESS) 09-09, School of Economics, University of East Anglia, Norwich, UK..
  • Handle: RePEc:uea:wcbess:09-09

    Download full text from publisher

    File URL:
    File Function: main text
    Download Restriction: no

    References listed on IDEAS

    1. Kaplan, Todd, et al, 2002. "All-Pay Auctions with Variable Rewards," Journal of Industrial Economics, Wiley Blackwell, vol. 50(4), pages 417-430, December.
    2. Yasar Barut & Dan Kovenock & Charles N. Noussair, 2002. "A Comparison of Multiple-Unit All-Pay and Winner-Pay Auctions Under Incomplete Information," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(3), pages 675-708, August.
    3. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, March.
    4. 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 289-294, March.
    5. Amegashie, J Atsu, 1999. "The Number of Rent-Seekers and Aggregate Rent-Seeking Expenditures: An Unpleasant Result," Public Choice, Springer, vol. 99(1-2), pages 57-62, April.
    6. Aloisio Araujo & Luciano Castro & Humberto Moreira, 2008. "Non-monotoniticies and the all-pay auction tie-breaking rule," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(3), pages 407-440, June.
    7. Arora, Ashish & Ceccagnoli, Marco & Cohen, Wesley M., 2008. "R&D and the patent premium," International Journal of Industrial Organization, Elsevier, vol. 26(5), pages 1153-1179, September.
    8. Dan Kovenock & Raymond J. Deneckere, 1996. "Bertrand-Edgeworth duopoly with unit cost asymmetry (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 1-25.
    9. Dan Kovenock & Michael R. Baye & Casper G. de Vries, 1996. "The all-pay auction with complete information (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 291-305.
    10. Amegashie, J. Atsu, 2001. "An all-pay auction with a pure-strategy equilibrium," Economics Letters, Elsevier, vol. 70(1), pages 79-82, January.
    11. Kaplan, Todd R. & Luski, Israel & Wettstein, David, 2003. "Innovative activity and sunk cost," International Journal of Industrial Organization, Elsevier, vol. 21(8), pages 1111-1133, October.
    12. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Oxford University Press, vol. 53(1), pages 1-26.
    13. Osborne, Martin J. & Pitchik, Carolyn, 1986. "Price competition in a capacity-constrained duopoly," Journal of Economic Theory, Elsevier, vol. 38(2), pages 238-260, April.
    14. Tullock, Gordon, 1997. "Where Is the Rectangle?," Public Choice, Springer, vol. 91(2), pages 149-159, April.
    15. Glenn C. Loury, 1979. "Market Structure and Innovation," The Quarterly Journal of Economics, Oxford University Press, vol. 93(3), pages 395-410.
    16. Wakelin, Katharine, 2001. "Productivity growth and R&D expenditure in UK manufacturing firms," Research Policy, Elsevier, vol. 30(7), pages 1079-1090, August.
    17. Bertoletti, Paolo, 2006. "On the reserve price in all-pay auctions with complete information and lobbying games," MPRA Paper 1083, University Library of Munich, Germany.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. BOS, Olivier & RANGER, Martin, 2009. "All-pay auctions with endogenous rewards," CORE Discussion Papers 2009059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Subhasish Chowdhury & Roman Sheremeta, 2015. "Strategically equivalent contests," Theory and Decision, Springer, vol. 78(4), pages 587-601, April.
    3. Subhashish Modak Chowdhury & Roman M. Sheremeta, 2009. "The equivalence of contests," Working Paper series, University of East Anglia, Centre for Behavioural and Experimental Social Science (CBESS) 09-06, School of Economics, University of East Anglia, Norwich, UK..
    4. Subhasish M. Chowdhury & Dongryul Lee & Iryna Topolyan, 2013. "The Max-Min Group Contest," University of East Anglia Applied and Financial Economics Working Paper Series 050, School of Economics, University of East Anglia, Norwich, UK..
    5. Kennedy, Matthew & Basu, Biswajit, 2014. "An analysis of the climate change architecture," Renewable and Sustainable Energy Reviews, Elsevier, vol. 34(C), pages 185-193.

    More about this item


    contests; all-pay auction; no-win; non-monotonicity; pure strategy;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:uea:wcbess:09-09. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Theodore Turocy). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.