Mathematical Preliminaries.- Investment, Strategy, and Uncertainty.- The Effect of Information Streams on Capital Budgeting Decisions.- Symmetric Equilibria in Game Theoretic Real Option Models.- The Effects of Information on Strategic Investment.- Cooperation, Spillovers, and Investment.- Spillovers and Strategic Cooperative Behaviour.- The Timing of Vertical Mergers Under Uncertainty.- Bounded Rationality and Market Evolution.- Multi-Level Evolution in Cournot Oligopoly.- Evolution of Conjectures in Cournot Oligopoly.- Bounded Rationality in a Finance Economy with Incomplete Markets.
Chapter 4 SYMMETRIC EQUILIBRIA IN GAME THEORETIC REAL OPTION MODELS (p. 77-78)
1. Introduction
The timing of an investment project is an important problem in capital budgeting. Many decision criteria have been proposed in the literature, the net present value (NPV) rule being the most famous one. In the past twenty years the real options literature emerged (cf. Dixit and Pindyck (1996)) in which uncertainty about the pro.tability of an investment project is explicitly taken into account. In the standard real option model the value of the investment project is assumed to follow a geometric Brownian motion. By solving the resulting optimal stopping problem one can show that it is optimal for the .rm to wait longer with investing than when the firm uses the NPV approach.
A natural extension of the one firm real option model is to consider a situation where several firms have the option to invest in the same project. Important fields of application of the game theoretic real options approach are R&D competition, technology adoption and new market models. Restricting ourselves to a duopoly framework, the aim of this chapter is to propose a method that solves the coordination problems which arise if there is a .rst mover advantage that creates a preemptive threat and, hence, erodes the option value. In the resulting preemption equilibrium, situations can occur where it is optimal for one firm to invest, but not for both. The coordination problem then is to determine which firm will invest. This problem is particularly of interest if both firms are ex ante identical. In the literature, several contributions (see Grenadier (2000) for an overview) solve this coordination problem by making explicit assumptions which are often unsatisfactory. In this chapter, we propose a method, based on Fudenberg and Tirole (1985), to solve the coordination problem endogenously.
The basic idea of the method is that one splits the game into a timing game where the preemption moment is determined and a game that is played either as soon as the preemption moment has been reached, or when the starting point is such that it is immediately optimal for one firm to invest but not for both. The outcome of the latter game determines which firm is the .rst investor. The .rst game is a game in continuous time where strategies are given by a cumulative distribution function. The second game is analogous to a repeated game in which firms play a fixed (mixed) strategy (invest or wait) until at least one firm invests.
As an illustration a simplified version of the model of Smets (1991) that is presented in Dixit and Pindyck (1996, Section 9.3), is analysed.
In the preemption equilibrium situations occur where it is optimal for one firm to invest, but at the same time investment is not beneficial if both firms decide to do so. Nevertheless, contrary to e.g. Smets (1991) and Dixit and Pindyck (1996), we .nd that there are scenarios in which both firms invest at the same time, which leads to a low payo. for both of them. We obtain that such a coordination failure can occur with positive probability at points in time where the payoff of the first investor, the leader, is strictly larger than the payo. of the other firm, the follower. From our analysis it can thus be concluded that Smets' statement that "if both players move simultaneously, each of them becomes leader with probability one half and follower with probability one half" (see Smets (1991, p. 12) and Dixit and Pindyck (1996, p. 313)) need not be true.
The point we make here extends to other contributions that include the real option framework in duopoly models. These papers, such as Grenadier (1996), Dutta et al. (1995), and Weeds (2002), make unsatisfactory assumptions with the aim to be able to ignore the possibility of simultaneous investment at points of time that this is not optimal. Grenadier (1996, pp. 1656-1657) assumes that "if each tries to build first, one will randomly (i.e., through the toss of a coin) win the race", while Dutta et al. (1995, p.568) assume that "If both [firms] i and j attempt to enter at any period t, then only one of them succeeds in doing so".
