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When are signals complements or substitutes?

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  • Tilman Borgers

    ()

  • Angel Hernando-Veciana

    ()

  • Daniel Krahmer

    ()

Abstract

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 special setting with a binary state space and binary, symmetric signals, we find an explicit characterization that permits an intuitive interpretation of complementarity and substitutability. We demonstrate how these conditions extend to the general case. Finally, we study implications of complementarity and substitutability for information acquisition and in a second price auction.

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Bibliographic Info

Paper provided by Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we072111.

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Date of creation: Mar 2007
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Handle: RePEc:cte:werepe:we072111

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  1. James Andreoni & Tymofiy Mylovanov, 2012. "Diverging Opinions," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 209-32, February.
  2. Jonathan Levin & Susan Athey, 2001. "The Value of Information in Monotone Decision Problems," Working Papers 01003, Stanford University, Department of Economics.
  3. Schmitz, Patrick W. & Tröger, Thomas, 2011. "The (sub-)optimality of the majority rule," MPRA Paper 32716, University Library of Munich, Germany.
  4. Miklos Sarvary & Philip M. Parker, 1997. "Marketing Information: A Competitive Analysis," Marketing Science, INFORMS, vol. 16(1), pages 24-38.
  5. 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.
  6. Nicola Persico, 2004. "Committee Design with Endogenous Information," Review of Economic Studies, Oxford University Press, vol. 71(1), pages 165-191.
  7. Péter Kondor, 2005. "The more we know, the less we agree: public announcements and higher-order expectations," FMG Discussion Papers dp532, Financial Markets Group.
  8. Nicola Persico, 2004. "Committee Design with Endogenous Information," Review of Economic Studies, Wiley Blackwell, vol. 71(1), pages 165-191, 01.
  9. Nicola Persico, 1997. "Information Acquisition in Auctions," UCLA Economics Working Papers 762, UCLA Department of Economics.
  10. 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.
  11. 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.
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