Dynamic Information Design: Two Examples

Abstracts:

joint with Laura Doval:
We take as given the set of agents, their set of actions, and their payoffs. We ask what distributions over actions are consistent with the players playing according to some extensive form. The main result of the paper is to show that a distribution over outcomes is implementable as a Perfect Bayesian equilibrium (PBE) of an admissible extensive form if, and only if, it is implementable as a PBE of a canonical extensive form. The la er is an admissible extensive form, in which there is a randomization device that not only sends (private) recommendations to the agents, but also selects the order in which the agents move; moreover, subsequent recommendations can be made conditional on actions already taken. This result strictly generalizes Aumann’s notion of correlated equilibrium, and Bergemann and Morris’ [3] notion of Bayes’ correlated equilibrium.

joint with Martin Szydlowski:
We study information as an incentive device in a dynamic moral hazard framework. An agent works on a project of uncertain difficulty, modeled as duration of required effort. The principal knows the task difficulty and can provide information over time with the goal of inducing maximal effort. The optimal mechanism features moving goalposts: an initial disclosure makes the agent sufficiently optimistic that the task is easy in order to induce him to start working. If the task is indeed difficult the agent is told this only after working long enough to put the difficult task within reach. Then the agent completes the difficult task even though he never would have chosen to at the outset. The optimal dynamic disclosure policy improves on any single-stage persuasion mechanism even though the fundamentals of the problem are all essentially static.