No.634 Option Exercise Games and the q Theory of Investment

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Option Exercise Games and the q Theory of Investment

Back and Paulsen (2009) advocate using closed-loop equilibria as the solution concept to characterize firm strategies for real option exercise games analyzed in Grenadier (2002). This approach allows a firm to respond to its competitor’s strategy, resulting in a Markov subgame perfect equilibrium. Back and Paulsen (2009) identify a closed-loop equilibrium where firms use the simple net present value rule as doing so forms mutually best responses. The resulting outcome is equivalent to a perfectly competitive scenario in which firms ignore the option value of waiting and make zero profits. We provide a rigorous definition of closed-loop equilibria and show that there exist two sets of (infinitely many) closed-loop equilibria associated with linear and nonlinear investment thresholds, respectively. In equilibrium, firms invest more quickly than in the open-loop equilibrium of Grenadier (2002) yet more slowly than in the perfectly competitive outcome, and consequently earn positive profits, confirming Back and Paulsen(2009)’s conjecture. Furthermore, we find that the highest option value among the closed-loop equilibria associated with the linear investment thresholds corresponds to the lowest investment speed, below which preemption becomes a profitable deviation.