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When are signals complements or substitutes?

  • Börgers, Tilman
  • Hernando-Veciana, Angel
  • Krähmer, Daniel

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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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 148 (2013)
Issue (Month): 1 ()
Pages: 165-195

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Handle: RePEc:eee:jetheo:v:148:y:2013:i:1:p:165-195
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  1. Péter Kondor, 2005. "The more we know, the less we agree: public announcements and higher-order expectations," FMG Discussion Papers dp532, Financial Markets Group.
  2. Nicola Persico, 2004. "Committee Design with Endogenous Information," Review of Economic Studies, Wiley Blackwell, vol. 71(1), pages 165-191, 01.
  3. James Andreoni & Tymofiy Mylovanov, 2012. "Diverging Opinions," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 209-32, February.
  4. Milgrom, Paul & Weber, Robert J., 1982. "The value of information in a sealed-bid auction," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 105-114, June.
  5. Miklos Sarvary & Philip M. Parker, 1997. "Marketing Information: A Competitive Analysis," Marketing Science, INFORMS, vol. 16(1), pages 24-38.
  6. 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.
  7. 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.
  8. Schmitz, Patrick W. & Tröger, Thomas, 2011. "The (sub-)optimality of the majority rule," MPRA Paper 32716, University Library of Munich, Germany.
  9. Timothy Feddersen & Wolfgang Pesendorfer, 1997. "Voting Behavior and Information Aggregation in Elections With Private Information," Levine's Working Paper Archive 1560, David K. Levine.
  10. Nicola Persico, 2000. "Information Acquisition in Auctions," Econometrica, Econometric Society, vol. 68(1), pages 135-148, January.
  11. Nicola Persico, 2004. "Committee Design with Endogenous Information," Review of Economic Studies, Oxford University Press, vol. 71(1), pages 165-191.
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