2018 Volume 61 Issue 1 Pages 18-39
A game with an incumbent and an entrant is considered. Each of them decides a timing of an investment into a new project. The profit flows of both firms involve two uncertain factors: (i) demand for the market observed only by the incumbent, and (2) fluctuation of the profit flow described by a geometric Brownian motion observed by both firms. The optimal timing of the investment of the incumbent under high demand is earlier than that under low demand, if the entrant's timing is fixed. However, the earlier investment of the incumbent may reveal information of high demand to the entrant, so that the early investment of the incumbent would accelerate the timing of the investment of the entrant. This earlier investment of the entrant reduces monopolistic profit of the incumbent before the investment of the entrant. Therefore, the incumbent under high demand may delay the timing of the investment strategically in order to hide the information. In the present paper, equilibria of this signaling game are characterized and sufficient conditions for the strategic behavior of the incumbent are obtained.
The values of both firms in equilibria are compared with the case of complete information and the welfare loss is investigated. I observe that the marginal profit in the duopoly for the high-demand incumbent is small the incumbent invests strategically, whereas the incumbent invests truthfully if marginal profit in the duopoly is sufficiently large. Strategic behavior of the incumbent is also observed when the investment cost or volatility of the incumbent is large or the investment cost of the entrant is small.