Posterior-Separable Costs and Menu Preferences

2025-11-12

AI Summary

This paper characterizes the preference structure of rational, attention-constrained agents facing menu choices, identifying necessary and sufficient conditions for behavioral representation via a posterior-separable cost function. Methodologically, it models preferences as a Bayesian persuasion problem and establishes equivalence between two axioms—Independence of Irrelevant Alternatives and Ignorance Equivalence—and the existence of a smooth posterior-separable cost function. When the cost function is prior-invariant, the axiom system implies uniform differentiability and yields a unique optimal information design strategy. The analysis leverages tools from convex analysis, particularly the hyperplane separation theorem, and joint directional differentiability. Contributions include: (i) the first rigorous equivalence result linking menu preferences to posterior-separable attention costs; (ii) a unified differentiability characterization under prior invariance; and (iii) analytical derivation of the optimal signaling policy.

Technology Category

• Knowledge Representation and Reasoning: Preferences
• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

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.

Problem

• Characterizing axioms for posterior-separable cost functions in rational inattention
• Linking menu preferences to Bayesian persuasion with unique hyperplane solutions
• Establishing conditions for uniformly posterior separable differentiable costs

Innovation

• Posterior-separable cost with smoothness condition
• Axioms enabling Bayesian persuasion solvability
• Uniform posterior separability under invariant priors