Quick or Persistent? Strategic Investment Demanding Versatility

TL;DR

This paper develops a dynamic duopoly model with strategic investment options, analyzing equilibrium behaviors like preemption and attrition, and providing explicit solutions for optimal stopping boundaries and investment likelihoods.

Contribution

It introduces a mixed strategy equilibrium framework for investment under uncertainty, explicitly characterizing the stopping boundary and equilibrium stopping rates in a complex dynamic setting.

Findings

Both preemption and attrition can occur in equilibrium.

Explicit characterization of the stopping boundary in the state space.

Positive probability of preemption even with stochastic strategies.

Abstract

In this paper we analyse a dynamic model of investment under uncertainty in a duopoly, in which each firm has an option to switch from the present market to a new market. We construct a subgame perfect equilibrium in mixed strategies and show that both preemption and attrition can occur along typical equilibrium paths. In order to determine the attrition region a two-dimensional constrained optimal stopping problem needs to be solved, for which we characterize the non-trivial stopping boundary in the state space. We explicitly determine Markovian equilibrium stopping rates in the attrition region and show that there is always a positive probability of eventual preemption, contrasting the deterministic version of the model. A simulation-based numerical example illustrates the model and shows the relative likelihoods of investment taking place in attrition and preemption regions.