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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. Azrieli, Yaron & Lehrer, Ehud, 2008. "The value of a stochastic information structure," Games and Economic Behavior, Elsevier, vol. 63(2), pages 679-693, July.
  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. Olivier Gossner & Penelope Hernandez & Abraham Neyman, 2004. "Optimal Use of Communication Resources," Discussion Paper Series dp377, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  4. Dean P. Foster & Sergiu Hart, 2007. "An Operational Measure of Riskiness," Discussion Paper Series dp454, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  5. Sergiu Hart, 2010. "Comparing Risks by Acceptance and Rejection," Discussion Paper Series dp531, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  6. Olivier Gossner, 2011. "Simple Bounds on the Value of a Reputation," Econometrica, Econometric Society, vol. 79(5), pages 1627-1641, 09.
  7. 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.
  8. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, March.
  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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