# 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

## 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 Working Papers with number halshs-00648884.

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Handle: RePEc:hal:wpaper:halshs-00648884

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## Related research

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

This paper has been announced in the following NEP Reports:

## References

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1. Binswanger, Hans P, 1981. "Attitudes toward Risk: Theoretical Implications of an Experiment in Rural India," Economic Journal, Royal Economic Society, vol. 91(364), pages 867-90, December.
2. Itzhak Gilboa & Ehud Lehrer, 1989. "The Value of Information -- An Axiomatic Approach," Discussion Papers 835, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
3. Azrieli, Yaron & Lehrer, Ehud, 2008. "The value of a stochastic information structure," Games and Economic Behavior, Elsevier, vol. 63(2), pages 679-693, July.
4. Charles A. Holt & Susan K. Laury, 2002. "Risk Aversion and Incentive Effects," American Economic Review, American Economic Association, vol. 92(5), pages 1644-1655, December.
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. Olivier Gossner & Penelope Hernandez & Abraham Neyman, 2004. "Optimal Use of Communication Resources," Discussion Paper Series dp377, The Center for the Study of Rationality, Hebrew University, Jerusalem.
7. Robert J. Aumann & Roberto Serrano, 2006. "An Economic Index of Riskiness," Working Papers 2006-20, Brown University, Department of Economics.
8. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-20, July.
9. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
10. Dean Foster & Sergiu Hart, 2007. "An Operational Measure of Riskiness," Levine's Bibliography 843644000000000095, UCLA Department of Economics.
11. Alvaro Sandroni, 2000. "Do Markets Favor Agents Able to Make Accurate Predicitions?," Econometrica, Econometric Society, vol. 68(6), pages 1303-1342, November.
12. Sims, Christopher A., 2003. "Implications of rational inattention," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 665-690, April.
13. Olivier Gossner, 2011. "Simple Bounds on the Value of a Reputation," Econometrica, Econometric Society, vol. 79(5), pages 1627-1641, 09.
14. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
15. Peng, Lin, 2005. "Learning with Information Capacity Constraints," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 40(02), pages 307-329, June.
16. Blume, Lawrence & Easley, David, 1992. "Evolution and market behavior," Journal of Economic Theory, Elsevier, vol. 58(1), pages 9-40, October.
17. Nicola Persico, 2000. "Information Acquisition in Auctions," Econometrica, Econometric Society, vol. 68(1), pages 135-148, January.
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