Waiting after the lower trigger: A Cournot Bertrand real option note

We study a perpetual entry problem in which an entrant chooses both when to enter and whether to enter through price or quantity competition against an incumbent that has already committed to quantity. The two entry modes are mutually exclusive and differ in sunk cost and discounted operating-profit coefficient. We focus on the case in which price entry is cheaper, while quantity entry is more profitable. Although price entry may then have the lower stand-alone trigger, crossing that trigger need not justify immediate entry. We provide a sufficient condition under which there exists a nonempty interval above the lower stand-alone trigger on which immediate entry in either mode is suboptimal. The entrant waits because delay preserves the option of entering later through the more profitable quantity mode. Thus, in a Cournot Bertrand environment with uncertainty and irreversibility, the choice of strategic variable is part of the real-options timing problem itself.