Advertisement

A note on rational inattention and rate distortion theory

  • Tommaso Denti
  • Massimo MarinacciEmail author
  • Luigi Montrucchio
Article
  • 39 Downloads

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.

Keywords

Rational inattention Information theory Rate distortion theory 

JEL Classification

D81 D83 C6 

Notes

Acknowledgements

Funding was provided by H2020 European Research Council (Grant No. 670337).

References

  1. Aliprantis, C.D., Border, K.C.: Infinite Dimensional Analysis, 3rd edn. Springer, Berlin (2006)Google Scholar
  2. Berger, T.: Rate Distortion Theory: A Mathematical Basis for Data Compression. Prentice-Hall, Upper Saddle River (1971)Google Scholar
  3. Berger, T., Gibson, J.D.: Lossy source coding. IEEE Trans. Inf. Theory 44, 2693–2723 (1998)CrossRefGoogle Scholar
  4. Cerreia-Vioglio, S., Maccheroni, F., Marinacci, M.: A characterization of probabilities with full support in metric spaces and its implications for Laplace method. J. Optim. Theory Appl. (2018, forthcoming)Google Scholar
  5. Cover, T.M., Thomas, J.A.: Elements of Information Theory, 3rd edn. Wiley, London (2006)Google Scholar
  6. Csiszar, I.: On an extremum problem of information theory. Stud. Sci. Math. Hung. 9, 57–71 (1974a)Google Scholar
  7. Csiszar, I.: On the computation of rate-distortion functions. IEEE Trans. Inf. Theory 20, 122–124 (1974b)CrossRefGoogle Scholar
  8. Dupuis, P., Ellis, R.S.: A Weak Convergence Approach to the Theory of Large Deviations. Wiley, London (1997)CrossRefGoogle Scholar
  9. Gallager, R.G.: Information Theory and Reliable Communication. Wiley, London (1968)Google Scholar
  10. Gallager, R.G.: Information Theory and Reliable Communication (Udine Course). Springer, Berlin (1972)CrossRefGoogle Scholar
  11. Hansen, L.P., Marinacci, M.: Ambiguity aversion and model misspecification: an economic perspective. Stat. Sci. 31, 511–515 (2016)CrossRefGoogle Scholar
  12. Mackowiak, B., Wiederholt, M.: Optimal sticky prices under rational inattention. Am. Econ. Rev. 99, 769–803 (2009)CrossRefGoogle Scholar
  13. Mackowiak, B., Matejka, F., Wiederholt, M.: Rational Inattention: A Disciplined Behavioral Model. Mimeo, New York City (2018)Google Scholar
  14. Matejka, F., McKay, A.: Rational inattention to discrete choices: a new foundation for the multinomial logit model. Am. Econ. Rev. 105, 272–298 (2015)CrossRefGoogle Scholar
  15. Paciello, L., Wiederholt, M.: Exogenous information, endogenous information, and optimal monetary policy. Rev. Econ. Stud. 81, 356–388 (2014)CrossRefGoogle Scholar
  16. Shannon, C.E.: Coding theorems for a discrete source with a fidelity criterion. IRE Natl. Conv. Record 4, 142–163 (1959)Google Scholar
  17. Sims, C.A.: Implications of rational inattention. J. Monet. Econ. 50, 665–690 (2003)CrossRefGoogle Scholar
  18. Van Nieuwerburgh, S., Veldkamp, L.: Information acquisition and under-diversification. Rev. Econ. Stud. 77, 779–805 (2010)CrossRefGoogle Scholar
  19. Yang, M.: Coordination with flexible information acquisition. J. Econ. Theory 158, 721–738 (2015)CrossRefGoogle Scholar

Copyright information

© Associazione per la Matematica Applicata alle Scienze Economiche e Sociali (AMASES) 2019

Authors and Affiliations

  1. 1.Department of EconomicsCornell UniversityIthacaUSA
  2. 2.Department of Decision Sciences and IGIERUniversità BocconiMilanItaly
  3. 3.Collegio Carlo AlbertoUniversità di TorinoTurinItaly

Personalised recommendations