Strategic Ignorance and Information Design

Abstract

We study information design in strategic settings when agents can publicly commit
to not view their private signals. Ignoring the constraints that agents must be willing
to view their signals may lead to substantial divergence between the designer’s
intent and actual outcomes, even in the case where the designer seeks to maximize
the agents' payoffs. We introduce the approprite equilibrium concept — robust correlated
equilibrium — and characterize implementable distributions over states and
actions. Requiring robustness to strategic ignorance can explain qualitative properties
that standard information design cannot: the designer may provide redundant or
even conterproductive information, asymmetric information structures may be strictly
optimal in symmetric environments, providing information conditional on players'
choices rather than all at once may hurt the designer, and communication between
players may help her. Optimality may require that players ignore their signals with
positive probability.

Keywords: incomplete information games, information design, robustness, strategic ignorance, Bayes correlated equilibrium

JEL Classification: C72, D82, D83