The All-Pay Auction with Non-Monotonic Payoff
ESRC Centre for Competition Policy Working Paper No. 10-6
23 Pages Posted: 8 Jul 2010 Last revised: 11 Sep 2020
Date Written: December 1, 2009
We analyse an endogenous prize all-pay auction under complete information where it is possible that none of the bidders wins and the winning payoff becomes non-monotonic in own bid. We derive the conditions for the existence of pure strategy equilibria and fully characterize the unique mixed strategy equilibrium when pure strategy equilibria do not exist. The highvaluation bidder places two distinct mass points in his equilibrium mixed strategy and the equilibrium support of the low-valuation bidder is not continuous. Under common valuation, in the equilibrium mixed strategy both bidders place mass points at the same point of the support. Possible applications are discussed.
Keywords: Contests, All-pay auction, No-win, Non-monotonicity, Pure Strategy
JEL Classification: C62, C72, D74, D44
Suggested Citation: Suggested Citation