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Entropy and the value of information for investors

  • Antonio Cabrales
  • Olivier Gossner
  • Roberto Serrano

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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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 661465000000000355.

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Date of creation: 06 Dec 2010
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Handle: RePEc:cla:levarc:661465000000000355
Contact details of provider: Web page: http://www.dklevine.com/

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  1. Sergiu Hart, 2011. "Comparing Risks by Acceptance and Rejection," Journal of Political Economy, University of Chicago Press, vol. 119(4), pages 617 - 638.
  2. Azrieli, Yaron & Lehrer, Ehud, 2008. "The value of a stochastic information structure," Games and Economic Behavior, Elsevier, vol. 63(2), pages 679-693, July.
  3. 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.
  4. Olivier Gossner, 2011. "Simple Bounds on the Value of a Reputation," Econometrica, Econometric Society, vol. 79(5), pages 1627-1641, 09.
  5. Olivier Gossner & Penélope Hernández & Abraham Neyman, 2006. "Optimal Use of Communication Resources," Econometrica, Econometric Society, vol. 74(6), pages 1603-1636, November.
  6. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
  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. Jonathan Levin & Susan Athey, 2001. "The Value of Information in Monotone Decision Problems," Working Papers 01003, Stanford University, Department of Economics.
  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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