Waiting Above the Lower Stand-Alone Trigger: A Cournot–Bertrand Real-Options Note

Abstract We study a Cournot–Bertrand entry problem where an entrant chooses both timing and mode – price or quantity – against a quantity-committed incumbent. The two modes are mutually exclusive and differ in sunk costs and profitability. While each mode alone yields a standard real-options threshold rule, this does not extend to the joint decision. Even if price competition is cheaper and has a lower stand-alone trigger, exceeding this threshold does not guarantee immediate entry. We provide a simple sufficient condition for a nonempty interval above the lower trigger where entry in either mode is suboptimal. In this region, the entrant delays to preserve the option of entering later via the more profitable quantity mode, which is irreversibly lost upon early entry. A numerical example illustrates the result. Thus, with mutually exclusive modes, standard threshold rules fail to characterize optimal entry timing.