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Strategic Irreversible Investment

Jan-Henrik Steg

Abstract

This paper studies oligopolistic irreversible investment with closed-loop strategies. These permit fully dynamic interactions that result in much richer strategic behavior than previous studies with open-loop strategies allow. The tradeoff between preemption incentives and the option value of waiting becomes distinctly visible. Strategies that depend on present capital stocks enable credible reactions that deter from excessive preemption and support positive option values in equilibrium. Simpler strategies lead into a "preemption trap" with perfectly competitive outcome and zero net present values. To obtain these results, a novel concept of Markov perfect equilibrium is developed that copes with optimal investment taking the form of singular control.

Strategic Irreversible Investment

Abstract

This paper studies oligopolistic irreversible investment with closed-loop strategies. These permit fully dynamic interactions that result in much richer strategic behavior than previous studies with open-loop strategies allow. The tradeoff between preemption incentives and the option value of waiting becomes distinctly visible. Strategies that depend on present capital stocks enable credible reactions that deter from excessive preemption and support positive option values in equilibrium. Simpler strategies lead into a "preemption trap" with perfectly competitive outcome and zero net present values. To obtain these results, a novel concept of Markov perfect equilibrium is developed that copes with optimal investment taking the form of singular control.

Paper Structure

This paper contains 13 sections, 19 theorems, 92 equations.

Table of Contents

  1. Introduction
  2. Model
  3. Equilibrium concept
  4. Solution approach
  5. Reflection strategies
  6. Verification theorem
  7. Application
  8. Static price triggers
  9. Dynamic price triggers
  10. Discussion
  11. Proof of Theorem \ref{['thm:ver']}
  12. Lemmas for the proof of Theorem \ref{['thm:static']}
  13. Lemmas for the proof of Theorem \ref{['thm:dynamic']}

Key Result

Theorem 1

Let $\phi^{1}$ and $\phi^{2}$ be reflection strategies with corresponding boundaries $\bar{X}^{1}$ and $\bar{X}^{2}$. Suppose there exists a differentiable function $V(x,q^{i},q^{-i})$ such that Then, for any given state $(x,q^{1},q^{2})$ and $X_0=x$, for any outcome from $(\phi^{1},\phi^{2})$ that satisfies and Furthermore, if $V$ has the additional properties that then, for any given state

Theorems & Definitions (38)

  • Definition 1
  • Theorem 1: Verification
  • Theorem 2
  • proof
  • Theorem 3
  • proof
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • ...and 28 more