Investment under Uncertainty, Coalition Spillovers and Market Evolution in a Game Theoretic Perspective / Theory and Decision Library C Bd.35 (PDF)

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".