# Continuous Time Contests with Private Information

Article

Mathematics of Operations Research

Issue number:

Vol. 41, Issue 3

Publisher:

Informs

Year:

2016

Journal pages:

1093-1107

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. We prove existence and uniqueness of a Nash equilibrium outcome and derive the equilibrium distribution in closed form. As the variance tends to zero, the equilibrium outcome converges to the symmetric equilibrium of an all-pay auction. For two players and constant costs, each playerâ€™s equilibrium profit decreases if the drift increases, the variance decreases, or the costs decrease.