Sequential all-pay auctions with head starts Academic Article uri icon

abstract

  • We study a sequential all-pay auction where heterogeneous contestants are privately informed about a parameter (ability) that a¤ects their cost of e¤ort. In the case of two contestants, contestant 1 (the …rst mover) makes an e¤ort in the …rst period, while contestant 2 (the second mover) observes the e¤ort of contestant 1 and then makes an e¤ort in the second period. Contestant 2 wins the contest if his e¤ort is larger than or equal to the e¤ort of contestant 1; otherwise, contestant 1 wins. This model is then generalized to any number of contestants where in each period of the contest, 1 j n, a new contestant joins and chooses an e¤ort. Contestant j observes the e¤orts of all contestants in the previous periods and then makes an e¤ort in period j: He wins if his e¤ort is larger than or equal to the e¤orts of all the contestants in the previous periods and strictly larger than the e¤orts of all the contestants in the following periods. This generalized model is studied also with a "stopping rule" according to which the contest ends as soon as a contestant exerts an e¤ort strictly smaller than the e¤ort of the previous contestant. We characterize the unique sub-game perfect equilibrium of these sequential all-pay auctions and analyze the use of head starts to improve the contestants'performances.

publication date

  • January 1, 2014