Strategic Ignorance and Information Design

摘要

We study information design in strategic settings when agents can publicly refuse to 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 appropriate equilibrium concept — ignorance-permissive Bayes correlated equilibrium — and characterize implementable distributions over states and actions. The designer’s optimal response to strategic ignorance generates qualitative properties that standard information design cannot: the designer may provide redundant or even counterproductive information, asymmetric information structures may be strictly optimal in symmetric environments, providing information conditional on players’ viewing choices rather than all at once may hurt the designer, and communication between players may help her. Optimality sometimes requires that players ignore their signals with positive probability.