Private Information Acquisition and Preemption: a Strategic Wald Problem

This paper studies a dynamic information acquisition model with payoff externalities. Two players can acquire costly information about an unknown state before taking a safe or risky action. Both information and the action taken are private. The first player to take the risky action has an advantage but whether the risky action is profitable depends on the state. The players face the tradeoff between being first and being right. In equilibrium, for different priors, there exist three kinds of randomisation: when the players are pessimistic, they enter the competition randomly; when the players are less pessimistic, they acquire information and then randomly stop; when the players are relatively optimistic, they randomly take an action without acquiring information.