Competition and Learning in Real Options

Abstract

We study a product development race by introducing competition under private information in an otherwise standard real-options environment. Firms observe the stochastic evolution of their own potential payoffs from entry into a market, while forming conjectures about the state of their opponents. They face a trade-off between immediate entry or delay, in which the costs of waiting are enhanced by the endogenous threat of preemption by a rival. We characterize Markov Perfect Equilibria through a coupled system of differential equations: forward-looking value functions determine optimal exercise rules, while backward-looking beliefs determine the probability of an opponent's exercise. The equilibrium displays an intensity of competition that first builds up, then subsides slowly towards a steady-state. We additionally compute the equilibrium and illustrate some of its qualitative properties, such as the long-lived transient dynamics and the consequences of heterogeneity between competitors.