Preemption Games Under Levy Uncertainty
47 Pages Posted: 15 May 2011
Date Written: May 14, 2011
We study a stochastic version of Fudenberg and Tirole's (1985) preemption game to analyze the effects of jumps in the underlying uncertainty on equilibrium strategies. Two firms contemplate entering a new market where the demand follows a jump-diffusion process. Firms differ is the sunk costs of entry. In the initial state, entry is optimal to none of the firms. If there are no upward jumps in the stochastic demand, then the low cost firm is the leader, and the high cost firm is the follower. In this case, if the cost disadvantage is sufficiently large, then a sequential equilibrium is played, where the low cost firm chooses the optimal entry threshold as a monopolist. If the cost disadvantage is sufficiently small, then a preemptive equilibrium occurs, where the low cost firm has to enter earlier than the optimal entry threshold of the monopolist is reached. If the demand process admits positive jumps, then the spectrum of equilibria changes dramatically; simultaneous entry can happen as an equilibrium, or as a coordination failure with positive probability; and sequential equilibrium may disappear. Also, the high cost firm may be the first to enter. We characterize subgame perfect equilibria using a natural generalization of the strategy spaces formalized in Fudenberg and Tirole's (1985). Strategies are described in terms of stopping times and value functions. Analytical expressions for the value functions and thresholds that define stopping times are derived.
Keywords: stopping time games, preemption, Levy uncertainty
JEL Classification: C73, C61, D81
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