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Entropy and the value of information for investors

  • Antonio Cabrales


    (Departamento de Economía - Universidad Carlos III de Madrid)

  • Olivier Gossner

    (PSE - Paris-Jourdan Sciences Economiques - CNRS - Institut national de la recherche agronomique (INRA) - EHESS - École des hautes études en sciences sociales - ENS Paris - École normale supérieure - Paris - École des Ponts ParisTech (ENPC), EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics, LSE - London School of Economics and Political Science - LSE)

  • Roberto Serrano

    (Department of Economics - Brown University, Institute IMDEA Software [Madrid] - Institute IMDEA Software)

Consider any investor who fears ruin when facing any set of investments that satisfy no-arbitrage. Before investing, he can purchase information about the state of nature in the form of an information structure. Given his prior, information structure $\alpha$ is more informative than information structure $\beta$ if, whenever he is willing to buy $\beta$ at some price, he is also willing to buy $\alpha$ 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.

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Paper provided by HAL in its series PSE Working Papers with number halshs-00648884.

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Date of creation: Dec 2011
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Handle: RePEc:hal:psewpa:halshs-00648884
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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. 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.
  3. 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).
  4. Olivier Gossner, 2011. "Simple Bounds on the Value of a Reputation," Econometrica, Econometric Society, vol. 79(5), pages 1627-1641, 09.
  5. Jonathan Levin & Susan Athey, 2001. "The Value of Information in Monotone Decision Problems," Working Papers 01003, Stanford University, Department of Economics.
  6. 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.
  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. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, July.
  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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