When are signals complements or substitutes?
The paper introduces a notion of complementarity (substitutability) of two signals which requires that in all decision problems each signal becomes more (less) valuable when the other signal becomes available. We provide a general characterization which relates complementarity and substitutability to a Blackwell comparison of two auxiliary signals. In a setting with a binary state space and binary signals, we find an explicit characterization that permits an intuitive interpretation of complementarity and substitutability. We demonstrate how these conditions extend to more general settings. We also illustrate the implications of our concepts for three economic applications: information disclosure in auctions, information aggregation through voting, and polarization of beliefs.
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References listed on IDEAS
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- Susan Athey & Jonathan Levin, 1998.
"The Value of Information In Monotone Decision Problems,"
98-24, Massachusetts Institute of Technology (MIT), Department of Economics.
- Jonathan Levin & Susan Athey, 2001. "The Value of Information in Monotone Decision Problems," Working Papers 01003, Stanford University, Department of Economics.
- Paul Milgrom & Robert J. Weber, 1981.
"The Value of Information in a Sealed-Bid Auction,"
462, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Nicola Persico, 1997.
"Information Acquisition in Auctions,"
UCLA Economics Working Papers
762, UCLA Department of Economics.
- Nicola Persico, 2004. "Committee Design with Endogenous Information," Review of Economic Studies, Oxford University Press, vol. 71(1), pages 165-191.
- Dow, James & Gorton, Gary, 1993. "Trading, Communication and the Response of Asset Prices to News," Economic Journal, Royal Economic Society, vol. 103(418), pages 639-46, May.
- Timothy Feddersen & Wolfgang Pesendorfer, 1997.
"Voting Behavior and Information Aggregation in Elections With Private Information,"
Levine's Working Paper Archive
1560, David K. Levine.
- Timothy Feddersen & Wolfgang Pesendorfer, 1997. "Voting Behavior and Information Aggregation in Elections with Private Information," Econometrica, Econometric Society, vol. 65(5), pages 1029-1058, September.
- Timothy Feddersen & Wolfgang Pesendorfer, 1994. "Voting Behavior and Information Aggregation in Elections with Private Information," Discussion Papers 1117, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Péter Kondor, 2005.
"The more we know, the less we agree: public announcements and higher-order expectations,"
FMG Discussion Papers
dp532, Financial Markets Group.
- Peter Kondor, 2004. "The more we know, the less we agree: public announcements and higher-order expectations," LSE Research Online Documents on Economics 24645, London School of Economics and Political Science, LSE Library.
- Miklos Sarvary & Philip M. Parker, 1997. "Marketing Information: A Competitive Analysis," Marketing Science, INFORMS, vol. 16(1), pages 24-38.
- James Andreoni & Tymofiy Mylovanov, 2012. "Diverging Opinions," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 209-32, February.
- Schmitz, Patrick W. & Tröger, Thomas, 2011.
"The (sub-)optimality of the majority rule,"
32716, University Library of Munich, Germany.
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