Posterior-Separable Costs and Menu Preferences

TL;DR

This paper characterizes when an agent's rationally inattentive preferences over menus can be represented by posterior-separable costs, using axioms that ensure smoothness and uniqueness in Bayesian persuasion models.

Contribution

It establishes necessary and sufficient axioms for posterior-separable costs in rational inattention, linking decision theory with Bayesian persuasion and differentiability conditions.

Findings

Axioms are necessary and sufficient for posterior-separable costs.

Invariance of costs across priors implies uniform posterior separability.

Differentiability of costs follows from the axioms under invariance.

Abstract

We consider an agent with a rationally inattentive preference over menus of acts, as in de Oliveira et al (2017). We show that two axioms, Independence of Irrelevant Alternatives and Ignorance Equivalence, are necessary and sufficient for this agent to have a posterior-separable cost satisfying a mild smoothness condition, called joint-directional differentiability. Viewing the decision-maker's problem as a Bayesian persuasion problem, we also show that these axioms are necessary and sufficient for solvability by a unique hyperplane. When the cost function remains invariant for different priors, we show that these axioms imply uniformly posterior separable costs that are differentiable.