The Indirect Cost of Information

TL;DR

This paper characterizes the class of indirect information costs derived from direct costs using sub-additivity, monotonicity, and posterior separability conditions, providing a comprehensive theoretical framework for understanding incremental evidence costs.

Contribution

It introduces a unified characterization of indirect information costs from direct costs using key conditions, advancing the theoretical understanding of information acquisition.

Findings

Characterizes indirect costs via sub-additivity and monotonicity.

Identifies conditions for posterior separability in indirect costs.

Provides necessary and sufficient conditions for prior independent costs.

Abstract

We study the indirect cost of information from sequential information cost minimization. A key sub-additivity condition, together with monotonicity equivalently characterizes the class of indirect cost functions generated from any direct information cost. Adding an extra (uniform) posterior separability condition equivalently characterizes the indirect cost generated from any direct cost favoring incremental evidences. We also provide the necessary and sufficient condition when prior independent direct cost generates posterior separable indirect cost.