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When are Signals Complements or Substitutes

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  • Tilman Borgers
  • Angel Hernanco-Veciana
  • Daniel Krohmer

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 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.

Suggested Citation

  • Tilman Borgers & Angel Hernanco-Veciana & Daniel Krohmer, 2010. "When are Signals Complements or Substitutes," Discussion Papers 1488, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:1488
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    Cited by:

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    3. James Andreoni & Tymofiy Mylovanov, 2012. "Diverging Opinions," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 209-232, February.
    4. Chade, Hector & Eeckhout, Jan, 2018. "Matching information," Theoretical Economics, Econometric Society, vol. 13(1), January.
    5. Mira Frick & Ryota Iijima & Yuhta Ishii, 2021. "Learning Efficiency of Multi-Agent Information Structures," Cowles Foundation Discussion Papers 2299, Cowles Foundation for Research in Economics, Yale University.
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    7. Deniz Kattwinkel & Axel Niemeyer & Justus Preusser & Alexander Winter, 2022. "Mechanisms without transfers for fully biased agents," Papers 2205.10910, arXiv.org.
    8. Mark Whitmeyer & Cole Williams, 2024. "Dynamic Signals," Papers 2407.16648, arXiv.org.
    9. Francesco Sangiorgi & Chester Spatt, 2017. "Opacity, Credit Rating Shopping, and Bias," Management Science, INFORMS, vol. 63(12), pages 4016-4036, December.
    10. Bergemann, Dirk & Ottaviani, Marco, 2021. "Information Markets and Nonmarkets," CEPR Discussion Papers 16459, C.E.P.R. Discussion Papers.
    11. ,, 2014. "On the relationship between individual and group decisions," Theoretical Economics, Econometric Society, vol. 9(1), January.
    12. Roland Strausz, 2024. "Correlation‐savvy sellers," RAND Journal of Economics, RAND Corporation, vol. 55(2), pages 266-291, June.
    13. Caio Machado & Ana Elisa Pereira, 2023. "Optimal Capital Structure with Stock Market Feedback," Review of Finance, European Finance Association, vol. 27(4), pages 1329-1371.
    14. Strausz, Roland, 2022. "Correlation-Savvy Sellers," Rationality and Competition Discussion Paper Series 347, CRC TRR 190 Rationality and Competition.
    15. 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.
    16. Ichihashi, Shota, 2021. "The economics of data externalities," Journal of Economic Theory, Elsevier, vol. 196(C).
    17. Joel Sobel, 2014. "On the relationship between individual and group decisions," Levine's Working Paper Archive 786969000000000950, David K. Levine.
    18. Deniz Kattwinkel & Axel Niemeyer & Justus Preusser & Alexander Winter, 2023. "Mechanisms without transfers for fully biased agents," CRC TR 224 Discussion Paper Series crctr224_2023_485, University of Bonn and University of Mannheim, Germany.

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    More about this item

    Keywords

    Complementarity; substitutability; value of information; Blackwell ordering.;
    All these keywords.

    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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