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American Economic Review Vol. 103 No. 1 2013

Entropy and the Value of Information for Investors

Antonio Cabrales1; Olivier Gossner2; Roberto Serrano3

1 Department of Economics, Universidad Carlos III de Madrid, Madrid 126, 28903 Getafe, Spain. · 2 Paris School of Economics—CNRS, 48 Boulevard Jourdan, 75014 Paris, France, and Department of Mathematics, London School of Economics. · 3 Department of Economics, Box B, Brown University, Providence, RI 02912.

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.

DOI
10.1257/aer.103.1.360
Volume
103
Issue
1
Pages
360-377
Language
en
Sources
openalex bibtex:phds-export.bib crossref

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