Racing Under Uncertainty: A Boundary Value Problem Approach

Abstract

In this paper I formulate a continuous time and continuous space version of Harris and Vickers (1987) Racing Under Uncertainty with potentially asymmetric players. To prove the existence and uniqueness of the equilibria, I use a boundary value problem formulation which is novel to the dynamic competition literature. In some cases, I obtain closed-form solutions of the equilibria in which equilibrium strategies exhibit the discouragement effect similar to the one in the original paper.