The Cost of Optimally Acquired Information

TL;DR

This paper develops a new framework for modeling the costs associated with acquiring information, emphasizing cost-minimization and recursive properties, with applications to rational inattention and new cost functions.

Contribution

It introduces a recursive characterization of indirect information costs, providing a foundation for analyzing and calculating these costs from primitive direct costs.

Findings

Characterized indirect costs by a novel recursive property.

Provided a tractable method to compute costs from direct costs.

Identified fundamental tradeoffs in rational inattention models.

Abstract

This paper introduces a framework for modeling the cost of information acquisition based on the principle of cost-minimization. We study the reduced-form \emph{indirect cost} of information generated by the sequential minimization of a primitive \emph{direct cost} function. Indirect cost functions: (i) are characterized by a novel recursive property, \emph{sequential learning-proofness}; (ii) provide an optimization foundation for the popular class of ``uniformly posterior separable'' costs; and (iii) can often be tractably calculated from their underlying direct costs. We apply the framework by identifying fundamental modeling tradeoffs in the rational inattention literature and two new indirect cost functions that balance these tradeoffs.