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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.

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File URL: http://mpra.ub.uni-muenchen.de/47587/1/MPRA_paper_47587.pdf
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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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  1. Ron Siegel, 2010. "Asymmetric Contests with Conditional Investments," American Economic Review, American Economic Association, vol. 100(5), pages 2230-60, December.
  2. 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.
  3. Baye, M.R. & Kovenock, D. & De Vries, C.G., 1991. "The All-Pay Auction With Complete Information," Purdue University Economics Working Papers 1007, Purdue University, Department of Economics.
  4. Olivier Bos & Martin Ranger, 2010. "All-Pay Auctions with Endogenous Rewards," Working Paper Series in Economics 46, University of Cologne, Department of Economics.
  5. Kaplan, T.R. & Luski, I. & Wettstein, D., 2000. "Innovative Activity and Sunk Cost," Discussion Papers 0006, Exeter University, Department of Economics.
  6. Arye L. Hillman & John G. Riley, 1987. "Politically Contestable Rents and Transfers," UCLA Economics Working Papers 452, UCLA Department of Economics.
  7. Amegashie, J. Atsu, 2001. "An all-pay auction with a pure-strategy equilibrium," Economics Letters, Elsevier, vol. 70(1), pages 79-82, January.
  8. Cohen, Chen & Kaplan, Todd & Sela, Aner, 2004. "Optimal Rewards in Contests," CEPR Discussion Papers 4704, C.E.P.R. Discussion Papers.
  9. Kaplan, Todd, et al, 2002. "All-Pay Auctions with Variable Rewards," Journal of Industrial Economics, Wiley Blackwell, vol. 50(4), pages 417-30, December.
  10. 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.
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