Racing under uncertainty: Boundary value problem approach

This paper explores the continuous time and continuous space model of racing under uncertainty put forward by Budd, Harris, and Vickers (1993) and allows for potentially asymmetric players. To prove the existence of Markov perfect equilibria, I use a boundary value problem formulation which is novel to the dynamic competition literature. In addition, by providing a new and intuitive definition of the pivot of an equilibrium, I show that equilibrium strategies exhibit the discouragement effect similar to that of Harris and Vickers (1987) but under a more general class of the cost functions.