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When are signals complements or substitutes?


  • Hernando-Veciana, Ángel
  • Börgers, Tilman
  • 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 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.

Suggested Citation

  • Hernando-Veciana, Ángel & Börgers, Tilman & Krähmer, Daniel, 2007. "When are signals complements or substitutes?," UC3M Working papers. Economics we072111, Universidad Carlos III de Madrid. Departamento de Economía.
  • Handle: RePEc:cte:werepe:we072111

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    References listed on IDEAS

    1. 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.
    2. Kondor, Peter, 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.
    3. James Andreoni & Tymofiy Mylovanov, 2012. "Diverging Opinions," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 209-232, 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. 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.
    6. Miklos Sarvary & Philip M. Parker, 1997. "Marketing Information: A Competitive Analysis," Marketing Science, INFORMS, pages 24-38.
    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, 2012. "The (sub-)optimality of the majority rule," Games and Economic Behavior, Elsevier, vol. 74(2), pages 651-665.
    9. Dow, James & Gorton, Gary, 1993. "Trading, Communication and the Response of Asset Prices to News," Economic Journal, Royal Economic Society, vol. 103(418), pages 639-646, May.
    10. Nicola Persico, 2000. "Information Acquisition in Auctions," Econometrica, Econometric Society, vol. 68(1), pages 135-148, January.
    11. repec:cup:apsrev:v:92:y:1998:i:02:p:413-418_21 is not listed on IDEAS
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    Cited by:

    1. James Andreoni & Tymofiy Mylovanov, 2012. "Diverging Opinions," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 209-232, February.
    2. Sobel, Joel, 2014. "On the relationship between individual and group decisions," Theoretical Economics, Econometric Society, vol. 9(1), January.
    3. Chade, Hector & Eeckhout, Jan, 2018. "Matching information," Theoretical Economics, Econometric Society, vol. 13(1), January.
    4. Martin Gregor, 2014. "Access fees for competing lobbies," Working Papers IES 2014/22, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Jul 2014.
    5. Joel Sobel, 2014. "On the relationship between individual and group decisions," Levine's Working Paper Archive 786969000000000950, David K. Levine.

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    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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