Preemption games under Lévy uncertainty

•We study effects of jumps in demand and firms' asymmetry on equilibrium strategies.•Without positive jumps, equilibrium strategies and types of equilibria are standard.•With positive jumps, equilibrium where low cost firm does not preempt may disappear.•Simultaneous entry can happen either as an equilibrium or a coordination failure.•High cost firm can become the leader.

We study a stochastic version of Fudenberg-Tirole's preemption game. Two firms contemplate entering a new market with stochastic demand. Firms differ in sunk costs of entry. If the demand process has no upward jumps, the low cost firm enters first, and the high cost firm follows. If leader's optimization problem has an interior solution, the leader enters at the optimal threshold of a monopolist; otherwise, the leader enters earlier than the monopolist. If the demand admits positive jumps, then the optimal entry threshold of the leader can be lower than the monopolist's threshold even if the solution is interior; simultaneous entry can happen either as an equilibrium or a coordination failure; the high cost firm can become the leader. We characterize subgame perfect equilibrium strategies in terms of stopping times and value functions. Analytical expressions for the value functions and thresholds that define stopping times are derived.