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When are Signals Complements or Substitutes

  • Tilman Borgers
  • Angel Hernanco-Veciana
  • Daniel Krohmer

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.

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File URL: http://www.kellogg.northwestern.edu/research/math/papers/1488.pdf
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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1488.

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Date of creation: 11 Apr 2010
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Handle: RePEc:nwu:cmsems:1488
Contact details of provider: Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014
Phone: 847/491-3527
Fax: 847/491-2530
Web page: http://www.kellogg.northwestern.edu/research/math/
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  1. Nicola Persico, 2004. "Committee Design with Endogenous Information," Review of Economic Studies, Wiley Blackwell, vol. 71(1), pages 165-191, 01.
  2. Susan Athey & Jonathan Levin, 1998. "The Value of Information In Monotone Decision Problems," Working papers 98-24, Massachusetts Institute of Technology (MIT), Department of Economics.
  3. Paul Milgrom & Robert J. Weber, 1981. "The Value of Information in a Sealed-Bid Auction," Discussion Papers 462, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Nicola Persico, 1997. "Information Acquisition in Auctions," UCLA Economics Working Papers 762, UCLA Department of Economics.
  5. 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.
  6. 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.
  7. Nicola Persico, 2004. "Committee Design with Endogenous Information," Review of Economic Studies, Oxford University Press, vol. 71(1), pages 165-191.
  8. Schmitz, Patrick W. & Tröger, Thomas, 2011. "The (sub-)optimality of the majority rule," MPRA Paper 32716, University Library of Munich, Germany.
  9. James Andreoni & Tymofiy Mylovanov, 2012. "Diverging Opinions," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 209-32, February.
  10. Miklos Sarvary & Philip M. Parker, 1997. "Marketing Information: A Competitive Analysis," Marketing Science, INFORMS, vol. 16(1), pages 24-38.
  11. Péter Kondor, 2005. "The more we know, the less we agree: public announcements and higher-order expectations," FMG Discussion Papers dp532, Financial Markets Group.
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