Bos, Olivier and Ranger, Martin (2013): All-Pay Auctions with Polynomial Rewards.
Download (425kB) | Preview
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.
|Item Type:||MPRA Paper|
|Original Title:||All-Pay Auctions with Polynomial Rewards|
|Keywords:||All-pay auctions, contests|
|Subjects:||D - Microeconomics > D4 - Market Structure, Pricing, and Design > D44 - Auctions
D - Microeconomics > D7 - Analysis of Collective Decision-Making > D72 - Political Processes: Rent-Seeking, Lobbying, Elections, Legislatures, and Voting Behavior
|Depositing User:||Olivier Bos|
|Date Deposited:||15. Jun 2013 09:29|
|Last Modified:||15. Jun 2013 09:39|
Amegashie, J. (2001): “An All-pay auction with a pure-strategy equilibrium,” Economics Letters, 70, 79–82.
Baye, M., D. Kovenock, and C. de Vries (1996): “The All-pay Auction with complete information,” Economic Theory, 8(2), 291–305.
Bos, O., and M. Ranger (2009): “All-pay auctions with endogenous rewards,” Working Paper Series in Economics, University of Cologne.
Che, Y.-K., and I. Gale (1998): “Caps on political Lobbying,” American Economic Review, 88, 643–651.
Che, Y.-K., and I. Gale (2006): “Caps on political Lobbying: Reply,” American Economic Review, 96, 1355–1360.
Chowdhury, S. (2009): “The All-pay Auction with Non-monotonic Payoff,” Purdue Uni- versity Working paper.
Cohen, C., T. Kaplan, and A. Sela (2009): “Optimal rewards in contests,” Rand Journal of Economics, forthcoming.
Hillman, A., and J. Riley (1989): “Politically contestable rents and transfers,” Economics and Policy, 1, 17–39.
Kaplan, T., I. Luski, A. Sela, and D. Wettstein (2002): “All-pay auctions with variable rewards,” Journal of Industrial Economics, 4, 417–430.
Kaplan, T., I. Luski, and D. Wettstein (2003): “Innovative Activity and Sunk Cost,” International Journal of Industrial Organisation, 21, 1111–1133.
Kaplan, T., and D. Wettstein (2006): “Caps on Political Lobbying: Comment,” Amer-ican Economic Review, 96(1351-1354).
Sacco, D., and A. Schumtzler (2008): “All-Pay Auctions with Negative Prize Externalities: Theory and Experimental Evidence,” University of Zurich, Socioeconomic Institute, Working Paper No. 0806.
Siegel, R. (2009): “All-Pay Contests,” Econometrica, 77, 71–92.
Siegel, R. (2010): “Asymmetric Contests with Conditional Investments,” American Economic Review, 100, 2230–2260.
Siegel, R. (2012): “Contests with Productive Effort,” mimeo.
Spanier, J., and K. Oldham (1987): An Atlas of Functions. Hemisphere Pubishing Corporation, Springer-Verlag.
Temme, N. (1996): Special Functions, An Introduction to the Classical Functions of Mathematical Physics. Wiley.
Vartiainen, H. (2007): “Comparing of all-pay auctions under complete information,” Review of Economic Design, forthcoming.