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 [4] 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 [10] but under a more general class of the cost functions.