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All-Pay Auctions with Polynomial Rewards

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  • Bos, Olivier
  • Ranger, Martin

Abstract

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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 47587.

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Date of creation: 11 May 2013
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Handle: RePEc:pra:mprapa:47587

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Keywords: All-pay auctions; contests;

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  1. Arye L. Hillman & John G. Riley, 1987. "Politically Contestable Rents and Transfers," UCLA Economics Working Papers, UCLA Department of Economics 452, UCLA Department of Economics.
  2. Todd Kaplan, 2001. "All-Pay Auctions with Variable Rewards," Discussion Papers, Exeter University, Department of Economics 0109, Exeter University, Department of Economics.
  3. Kovenock, D. & de Vries, C.G., 1995. "The All-Pay Auction with Complete Information," UFAE and IAE Working Papers, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) 311.95, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  4. Kaplan, Todd R. & Luski, Israel & Wettstein, David, 2003. "Innovative activity and sunk cost," International Journal of Industrial Organization, Elsevier, Elsevier, vol. 21(8), pages 1111-1133, October.
  5. Che, Yeon-Koo & Gale, Ian, 2006. "Caps on Political Lobbying: Reply," MPRA Paper 6097, University Library of Munich, Germany.
  6. Amegashie, J. Atsu, 2001. "An all-pay auction with a pure-strategy equilibrium," Economics Letters, Elsevier, Elsevier, vol. 70(1), pages 79-82, January.
  7. Olivier Bos & Martin Ranger, 2010. "All-Pay Auctions with Endogenous Rewards," Working Paper Series in Economics, University of Cologne, Department of Economics 46, University of Cologne, Department of Economics.
  8. Cohen, Chen & Kaplan, Todd & Sela, Aner, 2004. "Optimal Rewards in Contests," CEPR Discussion Papers, C.E.P.R. Discussion Papers 4704, C.E.P.R. Discussion Papers.
  9. Ron Siegel, 2010. "Asymmetric Contests with Conditional Investments," American Economic Review, American Economic Association, American Economic Association, vol. 100(5), pages 2230-60, December.
  10. Dario Sacco & Armin Schmutzler, 2008. "All-Pay Auctions with Negative Prize Externalities: Theory and Experimental Evidence," SOI - Working Papers, Socioeconomic Institute - University of Zurich 0806, Socioeconomic Institute - University of Zurich.
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