Private Information Acquisition and Preemption: a Strategic Wald Problem

TL;DR

This paper models a dynamic game where two players strategically acquire private information and decide when to act, balancing the benefits of being first against the accuracy of their information, with different equilibrium behaviors depending on prior beliefs.

Contribution

It introduces a novel strategic Wald problem with private information and payoff externalities, analyzing equilibrium behaviors and randomization in information acquisition and action timing.

Findings

Three types of equilibrium randomization identified

Players' strategies depend on their prior beliefs

Information acquisition and timing are strategically intertwined

Abstract

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.