# Entropy and the value of information for investors

## Author Info

• Antonio Cabrales

()

• Olivier Gossner

(PSE - Paris-Jourdan Sciences Economiques - CNRS : UMR8545 - École des Hautes Études en Sciences Sociales (EHESS) - École des Ponts ParisTech (ENPC) - École normale supérieure [ENS] - Paris - Institut national de la recherche agronomique (INRA), EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris, LSE - London School of Economics and Political Science - LSE)

• Roberto Serrano

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

Registered author(s):

## Abstract

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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## Bibliographic Info

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

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Handle: RePEc:hal:psewpa:halshs-00648884

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## Related research

Keywords: Informativeness ; Information structures ; Entropy ; Decision under uncertainty ; Investment ; Blackwell ordering;

Other versions of this item:

Find related papers by JEL classification:
• D14 - Microeconomics - - Household Behavior - - - Household Saving; Personal Finance
• D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
• D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
• G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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## References

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1. Susan Athey & Jonathan Levin, 1998. "The Value of Information In Monotone Decision Problems," Working papers, Massachusetts Institute of Technology (MIT), Department of Economics 98-24, Massachusetts Institute of Technology (MIT), Department of Economics.
2. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780195102680, October.
3. Sergiu Hart, 2010. "Comparing Risks by Acceptance and Rejection," Discussion Paper Series, The Center for the Study of Rationality, Hebrew University, Jerusalem dp531, The Center for the Study of Rationality, Hebrew University, Jerusalem.
4. Azrieli, Yaron & Lehrer, Ehud, 2008. "The value of a stochastic information structure," Games and Economic Behavior, Elsevier, Elsevier, vol. 63(2), pages 679-693, July.
5. Olivier Gossner & Penelope Hernandez & Abraham Neyman, 2004. "Optimal Use of Communication Resources," Discussion Paper Series, The Center for the Study of Rationality, Hebrew University, Jerusalem dp377, The Center for the Study of Rationality, Hebrew University, Jerusalem.
6. Olivier Gossner, 2011. "Simple Bounds on the Value of a Reputation," Econometrica, Econometric Society, Econometric Society, vol. 79(5), pages 1627-1641, 09.
7. Dean P. Foster & Sergiu Hart, 2009. "An Operational Measure of Riskiness," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 117(5), pages 785 - 814.
8. 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, American Economic Association, vol. 98(1), pages 38-71, March.
9. Blume, Lawrence & Easley, David, 1992. "Evolution and market behavior," Journal of Economic Theory, Elsevier, Elsevier, vol. 58(1), pages 9-40, October.
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## Citations

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Cited by:
1. Stark, Oded & Jakubek, Marcin & Falniowski, Fryderyk, 2014. "Reconciling the Rawlsian and the utilitarian approaches to the maximization of social welfare," Discussion Papers, University of Bonn, Center for Development Research (ZEF) 162881, University of Bonn, Center for Development Research (ZEF).
2. Kyungmin Kim & Benjamin Lester & Braz Camargo, 2012. "Subsidizing Price Discovery," 2012 Meeting Papers, Society for Economic Dynamics 338, Society for Economic Dynamics.
3. Camargo, Braz & Pastorino, Elena, 2012. "Career concerns: A human capital perspective," Textos para discussÃ£o 288, Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
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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