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Entropy and the Value of Information for Investors

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  • Antonio Cabrales
  • Olivier Gossner
  • Roberto Serrano

Abstract

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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Bibliographic Info

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. 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.
  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. Jonathan Levin & Susan Athey, 2001. "The Value of Information in Monotone Decision Problems," Working Papers 01003, Stanford University, Department of Economics.
  4. 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).
  5. Sergiu Hart, 2011. "Comparing Risks by Acceptance and Rejection," Journal of Political Economy, University of Chicago Press, vol. 119(4), pages 617 - 638.
  6. Dean P. Foster & Sergiu Hart, 2009. "An Operational Measure of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 117(5), pages 785 - 814.
  7. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
  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," Econometrica, Econometric Society, vol. 79(5), pages 1627-1641, 09.
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Cited by:
  1. Kyungmin Kim & Benjamin Lester & Braz Camargo, 2012. "Subsidizing Price Discovery," 2012 Meeting Papers 338, Society for Economic Dynamics.
  2. 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.
  3. Braz Camargo, 2011. "Career Concerns: A Human Capital Perspective," 2011 Meeting Papers 1274, Society for Economic Dynamics.
  4. Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2012. "The Appeal of Information Transactions," Economics Working Papers we1224, Universidad Carlos III, Departamento de Economía.

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