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Decisions in Economics and Finance

Erschienen in:

13.04.2019

A note on rational inattention and rate distortion theory

verfasst von: Tommaso Denti, Massimo Marinacci, Luigi Montrucchio

Erschienen in: Decisions in Economics and Finance | Ausgabe 1/2020

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Abstract

In this teaching note, we discuss the relation between rational inattention and a major branch of information theory called “rate distortion theory.” Focusing on methods, we translate tools from rate distortion theory into the language of rational inattention. These tools provide an alternative, more primitive, approach to the study of optimal attention allocation.

Vorheriger Artikel Semilattices, canonical embeddings and representing measures

Nächster Artikel Decisions on production and quality

See Mackowiak et al. (2018) for a recent survey of rational inattention.

Concavity is a consequence of the convexity of the mapping \((\nu ,\nu ^{\prime })\rightarrow \)\(D(\nu \Vert \nu ^{\prime })\). Properness follows from the hypothesis that \(k(\cdot ,y)\) is \(\mu \)-integrable for some \(y\in Y\) .

We have not proved yet that the solution sets are nonempty. We will do it later on in Proposition 7 under additional regularity assumptions.

Here \(\nu _{\tau }\) is the barycenter of \(\tau \). A standard textbook reference for mutual information, entropy, and related notions is chapter 2 of Cover and Thomas (2006).

Textbook references for rate distortion theory are Berger (1971) and chapter 10 of Cover and Thomas (2006). A comprehensive survey is Berger and Gibson (1998) .

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Mackowiak, B., Wiederholt, M.: Optimal sticky prices under rational inattention. Am. Econ. Rev. 99, 769–803 (2009)CrossRef

Mackowiak, B., Matejka, F., Wiederholt, M.: Rational Inattention: A Disciplined Behavioral Model. Mimeo, New York City (2018)

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Titel: A note on rational inattention and rate distortion theory
verfasst von: Tommaso Denti
Massimo Marinacci
Luigi Montrucchio
Publikationsdatum: 13.04.2019
Verlag: Springer International Publishing
Erschienen in: Decisions in Economics and Finance / Ausgabe 1/2020
Print ISSN: 1593-8883
Elektronische ISSN: 1129-6569
DOI: https://doi.org/10.1007/s10203-019-00243-0

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