Continuous Time Contests with Private Information
28 Pages Posted: 28 May 2011 Last revised: 28 Jun 2013
Date Written: June 26, 2013
This paper introduces a class of contest models in which each player decides when to stop a privately observed Brownian motion with drift and incurs costs depending on his stopping time. The player who stops his process at the highest value wins a prize. Potential applications include job promotion contests and procurement contests.
We prove existence and uniqueness of a Nash equilibrium outcome and derive the equilibrium distribution in closed form. If the noise vanishes, the equilibrium outcome converges to --- and thus selects --- the symmetric equilibrium outcome of an all-pay auction.
For two players and constant costs, each player's equilibrium profits decrease if all players are more productive. Intuitively, patience becomes a more important factor for contest success, which reduces informational rents.
Keywords: Contests, All-Pay Auctions, Silent Timing Games
JEL Classification: C72, C73, D81
Suggested Citation: Suggested Citation