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Entropy and the value of information for investors

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  • Antonio Cabrales

    ()
    (Universidad Carlos III de Madrid)

  • Olivier Gossner

    ()
    (Paris School of Economics and LSE)

  • Roberto Serrano

    ()
    (Brown University and IMDEA Social Sciences Institute)

Abstract

Consider any investor who fears ruin 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 rejects alpha at some price, he also rejects beta 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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Bibliographic Info

Paper provided by Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales in its series Working Papers with number 2010-23.

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Date of creation: 06 Dec 2010
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Publication status: Forthcoming in American Economic Review
Handle: RePEc:imd:wpaper:wp2010-23

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Keywords: informativeness; information structures; entropy; decision under uncertainty; investment; Blackwell ordering;

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References

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  1. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, September.
  2. Yaron Azrieli & Ehud Lehrer, 2004. "The Value Of A Stochastic Information Structure," Game Theory and Information 0411006, EconWPA.
  3. Olivier Gossner, 2011. "Simple Bounds on the Value of a Reputation," Econometrica, Econometric Society, vol. 79(5), pages 1627-1641, 09.
  4. 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.
  5. Blume, Lawrence & Easley, David, 1992. "Evolution and market behavior," Journal of Economic Theory, Elsevier, vol. 58(1), pages 9-40, October.
  6. 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).
  7. Dean P. Foster & Sergiu Hart, 2007. "An Operational Measure of Riskiness," Discussion Paper Series dp454, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  8. Sergiu Hart, 2011. "Comparing Risks by Acceptance and Rejection," Journal of Political Economy, University of Chicago Press, vol. 119(4), pages 617 - 638.
  9. 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.
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Cited by:
  1. Camargo, Braz & Pastorino, Elena, 2012. "Career concerns: A human capital perspective," Textos para discussão 288, Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
  2. Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2012. "The Appeal of Information Transactions," Working Papers 2012-13, Brown University, Department of Economics.
  3. Stark, Oded & Jakubek, Marcin & Falniowski, Fryderyk, 2013. "Reconciling the Rawlsian and the utilitarian approaches to the maximization of social welfare," University of Tuebingen Working Papers in Economics and Finance 65, University of Tuebingen, Faculty of Economics and Social Sciences.
  4. Kyungmin Kim & Benjamin Lester & Braz Camargo, 2012. "Subsidizing Price Discovery," 2012 Meeting Papers 338, Society for Economic Dynamics.

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