Blackwell-Monotone Information Costs

2024-04-23

Social Science Research Network

AI Summary

This paper investigates the monotonicity of information cost functions under the Blackwell information order: under what conditions does a more informative experiment necessarily incur higher cost? Using tools from convex analysis and differential inequalities, we establish the first necessary and sufficient characterization of Blackwell-monotone cost functions—namely, a system of linear differential inequalities. We further prove that an additive separable cost function is Blackwell-monotone if and only if each component is sublinear. This result unifies and generalizes several widely used cost structures—including entropy-based costs and sampling costs—and extends their applicability to bargaining and persuasion games. By grounding information design in economically interpretable cost assumptions, our characterization significantly enhances both the theoretical coherence and empirical relevance of information-theoretic models in economics.

Technology Category

• Game Theory and Economic Paradigms: Imperfect Information
• Machine Learning: Information Theory
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems
• Security and Privacy: Large-scale security measurements

Abstract

A Blackwell-monotone information cost function assigns higher costs to Blackwell more informative experiments. This paper provides simple necessary and sufficient conditions for a cost function to be Blackwell monotone over finite experiments. The key condition involves a system of linear differential inequalities. By using this characterization, we show that when a cost function is additively separable, it is Blackwell monotone if and only if it is the sum of sublinear functions. This identifies a wide range of practical information cost functions. Finally, we apply our results to bargaining and persuasion problems with costly information, broadening and strengthening earlier findings.

Problem

• Study monotonicity of information costs
• Establish conditions for cost function monotonicity
• Evaluate known cost functions using criteria

Innovation

• Study monotonicity of information costs
• Use Blackwell and Lehmann information orders
• Analyze cost functions with garbling conditions