∗A Multi-stage Investment Game in Real Option Analysis†

This paper investigates an interaction between the managerial flexibility and the competition in a dynamic situation. The value of the flexibility can be valued as a real option while the competition can be analyzed with the game theory. We consider a multi-stage game with two firms under demand uncertainty. In the model, One firm called firm L firstly makes an investment decision, and the other firm called firm F decides secondly after observing firm L’s decision at each stage. The model developed here is an extension of the two-stage investment game of Imai and Watanabe(2005), which fully characterize the equilibrium strategies for the two competitive firms by their investment costs. We show that the project values for both firms can be considered as a special example of switching options, and hence these values can be evaluated by the extended switching option model. We apply a binomial or a trinomial lattice to the underlying demand process. Although the lattice model is discrete it is a well-known fact that the trinomial process can converge efficiently to the continuoustime process if parameter values of the lattice model are carefully chosen and the number of trading periods tends to infinity. Hence our model can be also considered as an approximation of the continuous-time model. This paper analyzes equilibrium strategies and project values of the two competitive firms quantitatively under more realistic situations. In addition, by comparing our model with the two-stage game we can investigate the effects of multiple decision opportunities under a more realistic demand process. ∗This is a draft version of the research. We have changed many notations for consistency and simplicity. †Both authors acknowledge a research support from Grant-in-Aid for Scientific Research in Japan Society for the Promotion of Science. ‡Faculty of Policy Studies, Iwate Prefectural University(IPU), 152-52 Takizawa-aza-sugo Takizawa Iwate, JAPAN. Email:imai@iwate-pu.ac.jp §Faculty of Economics, Tokyo Metropolitan University, 1-1 Minami-Osawa Hachioji, Tokyo, JAPAN. Email: nabe@nabenavi.net