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Entropy and the Value of Information for Investors

  • Antonio Cabrales
  • Olivier Gossner
  • Roberto Serrano

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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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. Olivier Gossner & Pénélope Hernández & Abraham Neyman, 2006. "Optimal use of communication resources," Post-Print halshs-00754118, HAL.
  2. Jonathan Levin & Susan Athey, 2001. "The Value of Information in Monotone Decision Problems," Working Papers 01003, Stanford University, Department of Economics.
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  4. Yaron Azrieli & Ehud Lehrer, 2004. "The Value Of A Stochastic Information Structure," Game Theory and Information 0411006, EconWPA.
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  6. Charles A. Holt & Susan K. Laury, 2002. "Risk Aversion and Incentive Effects," American Economic Review, American Economic Association, vol. 92(5), pages 1644-1655, December.
  7. 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.
  8. Blume, Lawrence & Easley, David, 1992. "Evolution and market behavior," Journal of Economic Theory, Elsevier, vol. 58(1), pages 9-40, October.
  9. Olivier Gossner, 2011. "Simple bounds on the value of a reputation," Post-Print halshs-00654683, HAL.
  10. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, December.
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