Optimal Stopping Game with Investment Spillover Effect for Energy Infrastructure

The purpose of this study is to analyze the consequence of the existence of positive externality in the optimal choice of a firm’s time of investment in a gaming environment. I consider a situation where firms can increase their subsequent revenue stream by investing at a period of time. The investment opportunity is assumed to be one-time opportunity and once it is made, it cannot be redone, i.e., the investment is irreversible. This indicates that the choice of optimal time of investment is formulated as a so-called “optimal stopping problem” in mathematics. Moreover, I assume that the investment has a spillover effect to other firms. Namely, once a firm makes an expensive investment, all other firms can obtain the same result of the investment at no cost from the next time period. This positive externality allows firms to enter the game of identifying their own optimal investment time vis-à-vis their opponent’s choice of time.