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Entropy and the Value of Information for Investors

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  • Antonio Cabrales
  • Olivier Gossner
  • Roberto Serrano

Abstract

Consider an investor who fears ruin when facing investments that satisfy no-arbitrage. Before investing he can purchase information about the state of nature as an information structure. Given his prior, information structure α investment dominates information structure β if, whenever he is willing to buy β at some price, he is also willing to buy α at that price. We show that this informativeness ordering is complete and is represented by the decrease in entropy of his beliefs, regardless of his preferences, initial wealth, or investment problem. We also show that no prior-independent informativeness ordering based on similar premises exists. (JEL D14, D81, D83, G11)

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File URL: http://www.aeaweb.org/articles.php?doi=10.1257/aer.103.1.360
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File URL: http://www.aeaweb.org/aer/data/feb2013/20111176_app.pdf
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Bibliographic Info

Article provided by American Economic Association in its journal American Economic Review.

Volume (Year): 103 (2013)
Issue (Month): 1 (February)
Pages: 360-77

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Handle: RePEc:aea:aecrev:v:103:y:2013:i:1:p:360-77

Note: DOI: 10.1257/aer.103.1.360
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  1. Dean Foster & Sergiu Hart, 2007. "An Operational Measure of Riskiness," Levine's Bibliography 843644000000000095, UCLA Department of Economics.
  2. 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.
  3. Blume, Lawrence & Easley, David, 1992. "Evolution and market behavior," Journal of Economic Theory, Elsevier, vol. 58(1), pages 9-40, October.
  4. Yaron Azrieli & Ehud Lehrer, 2004. "The Value Of A Stochastic Information Structure," Game Theory and Information 0411006, EconWPA.
  5. Sergiu Hart, 2011. "Comparing Risks by Acceptance and Rejection," Journal of Political Economy, University of Chicago Press, vol. 119(4), pages 617 - 638.
  6. Olivier Gossner, 2011. "Simple Bounds on the Value of a Reputation," Econometrica, Econometric Society, vol. 79(5), pages 1627-1641, 09.
  7. 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).
  8. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
  9. Susan Athey & Jonathan Levin, 1998. "The Value of Information In Monotone Decision Problems," Working papers 98-24, Massachusetts Institute of Technology (MIT), Department of Economics.
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Citations

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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. Braz Camargo, 2011. "Career Concerns: A Human Capital Perspective," 2011 Meeting Papers 1274, Society for Economic Dynamics.
  3. Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2012. "The Appeal of Information Transactions," Working Papers 2012-13, Brown University, Department of Economics.
  4. Braz Camargo & Kyungmin (Teddy) Kim & Benjamin Lester, 2013. "Subsidizing price discovery," Working Papers 13-20, Federal Reserve Bank of Philadelphia.

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