Essays on timing and identification in a duopoly
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Upon making an optimal timing decision, a player takes into consideration not only the actions of the other players, but also the uncertainty of the environment. I use the real options approach to study the strategic timing decisions of asymmetric firms in an environment with uncertainty. When firms make timing decisions, they take into account the opportunity cost of immediate action today. The second chapter studies the identification in an asymmetric duopoly. The two potential entrants contemplate entering a new market where the demand follows a geometric Brownian motion. I show that under certain parameter conditions there will be an equilibrium triggered by preemption, and both firms could preempt. Moreover, the equilibrium may no longer be only triggered by preemption. I identify the joint distribution of the unobserved investment costs and find the probability of the first entry being triggered by preemption. Given the observation of the first entrant, I can predict the probability of observing the second entrant. The third chapter studies the spillover effect of exit in a vertical relationship. I extend the methodology of irreversible investment under uncertainty to consider exits in a vertical market structure. When the exogenous demand shock is low, one party of the supply chain wants to exit first and will thus lead to the exit of the remaining party. The firm which wants to exit later strategically acts to delay the exit of its counterpart and therefore prevents its own exit. When the state level drops below the unique equilibrium exit threshold, both firms will exit simultaneously. The expected delay in exit timing is derived. The fourth chapter studies the strategic optimal timing of entry in the competition between one-way essential complements under demand uncertainty. The value of a new add-on to its consumers is uncertain. While the rational essential good producing firm recognizes the value of waiting under uncertainty when it contemplates entering the add-on market and endogenously self-selects between the two entry options- to produce or to acquire, the add-on producing firm strategically decides when to agree on acquisition. The impact of profit sharing in the case of acquisition and relative fixed costs of entry on the size and form of the waiting region and the responses of both firms are analyzed.