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Entropy and the value of information for investors

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  • Antonio Cabrales
  • Olivier Gossner
  • Roberto Serrano

Abstract

Consider any investor who fears ruin facing any set of investments that satisfy noarbitrage. Before investing, he can purchase information about the state of nature in the form of an information structure. Given his prior, information structure α is more informative than information structure β if whenever he rejects α at some price, he also rejects β at that price. We show that this complete informativeness ordering is represented by the decrease in entropy of his beliefs, regardless of his preferences, initial wealth or investment problem. It is also shown that no prior-independent informativeness ordering based on similar premises exists.

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Bibliographic Info

Paper provided by Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we1104.

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Date of creation: Mar 2011
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Handle: RePEc:cte:werepe:we1104

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Keywords: Informativeness; Information structures; Entropy; Decision under uncertainty; Investment; Blackwell ordering;

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  1. Olivier Gossner, 2011. "Simple Bounds on the Value of a Reputation," Econometrica, Econometric Society, vol. 79(5), pages 1627-1641, 09.
  2. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, September.
  3. Sergiu Hart, 2010. "Comparing Risks by Acceptance and Rejection," Discussion Paper Series dp531, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  4. Thierry Post & Martijn J. van den Assem & Guido Baltussen & Richard H. Thaler, 2008. "Deal or No Deal? Decision Making under Risk in a Large-Payoff Game Show," American Economic Review, American Economic Association, vol. 98(1), pages 38-71, March.
  5. Olivier Gossner & Abraham Neyman & Penélope Hernández, 2005. "Optimal Use Of Communication Resources," Working Papers. Serie AD 2005-06, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  6. Jonathan Levin & Susan Athey, 2001. "The Value of Information in Monotone Decision Problems," Working Papers 01003, Stanford University, Department of Economics.
  7. Dean Foster & Sergiu Hart, 2007. "An Operational Measure of Riskiness," Levine's Bibliography 843644000000000095, UCLA Department of Economics.
  8. Yaron Azrieli & Ehud Lehrer, 2004. "The Value Of A Stochastic Information Structure," Game Theory and Information 0411006, EconWPA.
  9. Blume, Lawrence & Easley, David, 1992. "Evolution and market behavior," Journal of Economic Theory, Elsevier, vol. 58(1), pages 9-40, October.
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Cited by:
  1. Stark, Oded & Jakubek, Marcin & Falniowski, Fryderyk, 2014. "Reconciling the Rawlsian and the utilitarian approaches to the maximization of social welfare," Economics Letters, Elsevier, vol. 122(3), pages 439-444.
  2. Camargo, Braz & Pastorino, Elena, 2012. "Career concerns: A human capital perspective," Textos para discussão 288, Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
  3. Braz Camargo & Kyungmin (Teddy) Kim & Benjamin Lester, 2013. "Subsidizing price discovery," Working Papers 13-20, Federal Reserve Bank of Philadelphia.
  4. Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2012. "The Appeal of Information Transactions," Economics Working Papers we1224, Universidad Carlos III, Departamento de Economía.

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