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All-Pay Auctions with Polynomial Rewards


  • Bos, Olivier
  • Ranger, Martin


This paper examines a perfectly discriminating contest (all-pay auction) with two asymmetric players. We focus on unordered valuations. Valuations are endogenous (polynomial functions) and depend on the effort each player invests in the contest. The shape of the valuation function is common knowledge and differs between the contestants. Some key properties of R&D races, lobbying activity and sport contests are captured by this framework. After analyzing the unique mixed strategy equilibrium, we derive a closed form of the expected expenditure of both players. We characterize the expected expenditure by means of incomplete Beta functions.

Suggested Citation

  • Bos, Olivier & Ranger, Martin, 2013. "All-Pay Auctions with Polynomial Rewards," MPRA Paper 47587, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:47587

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    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. 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).
    3. 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.
    4. Amegashie, J. Atsu, 2001. "An all-pay auction with a pure-strategy equilibrium," Economics Letters, Elsevier, vol. 70(1), pages 79-82, January.
    5. Yeon-Koo Che & Ian L. Gale, 2006. "Caps on Political Lobbying: Reply," American Economic Review, American Economic Association, vol. 96(4), pages 1355-1360, September.
    6. 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.
    7. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, March.
    8. Ron Siegel, 2010. "Asymmetric Contests with Conditional Investments," American Economic Review, American Economic Association, vol. 100(5), pages 2230-2260, December.
    9. Dario Sacco & Armin Schmutzler, 2008. "All-Pay Auctions with Negative Prize Externalities: Theory and Experimental Evidence," SOI - Working Papers 0806, Socioeconomic Institute - University of Zurich.
    10. Chen Cohen & Todd R. Kaplan & Aner Sela, 2008. "Optimal rewards in contests," RAND Journal of Economics, RAND Corporation, vol. 39(2), pages 434-451.
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    More about this item


    All-pay auctions; contests;

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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