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All-Pay Auctions with Polynomial Rewards

Olivier Bos and Martin Ranger
Annals of Economics and Statistics
No. 115/116, SPECIAL ISSUE ON KNOWLEDGE CAPITAL IN NANOTECHNOLOGY AND OTHER HIGH TECHNOLOGY INDUSTRIES (December 2014), pp. 361-377
Published by: GENES on behalf of ADRES
DOI: 10.15609/annaeconstat2009.115-116.361
Stable URL: http://www.jstor.org/stable/10.15609/annaeconstat2009.115-116.361
Page Count: 17
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All-Pay Auctions with Polynomial Rewards
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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. JEL: D44, D72 / KEY WORDS: All-Pay Auctions, Contests

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