Attention elasticities and invariant information costs

TL;DR

This paper generalizes rational inattention by using information radius costs, introduces attention elasticity to measure sensitivity to incentives, and develops an efficient algorithm for optimal attention strategies.

Contribution

It introduces a new class of information costs controlling attention elasticity and provides an algorithm for computing optimal attention strategies.

Findings

Attention elasticity can be controlled by the choice of cost functions.

The Shannon model restricts attention elasticity to be one.

An efficient algorithm similar to Blahut-Arimoto is proposed for optimization.

Abstract

We consider a generalization of rational inattention problems by measuring costs of information through the information radius (Sibson, 1969; Verd\'u, 2015) of statistical experiments. We introduce a notion of attention elasticity measuring the sensitivity of attention strategies with respect to changes in incentives. We show how the introduced class of cost functions controls attention elasticities while the Shannon model restricts attention elasticity to be unity. We explore further differences and similarities relative to the Shannon model in relation to invariance, posterior separability, consideration sets, and the ability to learn events with certainty. Lastly, we provide an efficient alternating minimization method -- analogous to the Blahut-Arimoto algorithm -- to obtain optimal attention strategies.