Optimal Information Disclosure in a Stackelberg Game

Abstract

We investigate a leader-follower game in which the leader hires the follower to complete a project with the presence of a random shock time. If the project is completed before the shock time, then both players receive (up to discounting) $1 each. If it is completed after the shock time, then the leader and the follower receive $y and $x respectively. The shock time is observable by the leader, but not by the follower. The leader chooses how to reveal the information of the shock time, and the follower controls the effort level which affects the project completion time. The goal is to find the leader’s value and optimal information disclosure strategy. By considering the leader’s value as a function of the follower’s utility as well as the follower’s belief about the shock time, we characterize the leader’s value using dynamic programming equations. The leader’s (ε-)optimal strategy can also be constructed from these equations.