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When are signals complements or substitutes?

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

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. We also illustrate the implications of our concepts for three economic applications: information disclosure in auctions, information aggregation through voting, and polarization of beliefs.

Suggested Citation

  • Börgers, Tilman & Hernando-Veciana, Angel & Krähmer, Daniel, 2013. "When are signals complements or substitutes?," Journal of Economic Theory, Elsevier, vol. 148(1), pages 165-195.
    • Handle: RePEc:eee:jetheo:v:148:y:2013:i:1:p:165-195
    DOI: 10.1016/j.jet.2012.12.012
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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.
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    7. Federico Vaccari, 2024. "Belief patterns with information processing," Papers 2411.17597, arXiv.org.
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    9. Deniz Kattwinkel & Axel Niemeyer & Justus Preusser & Alexander Winter, 2022. "Mechanisms without transfers for fully biased agents," Papers 2205.10910, arXiv.org.
    10. Mark Whitmeyer & Cole Williams, 2024. "Dynamic Signals," Papers 2407.16648, arXiv.org.
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    13. ,, 2014. "On the relationship between individual and group decisions," Theoretical Economics, Econometric Society, vol. 9(1), January.
    14. Jan Knoepfle, 2024. "Dynamic Competition for Attention," Papers 2409.18595, arXiv.org, revised Oct 2024.
    15. Kailin Chen, 2025. "Experiments in the Linear Convex Order," Papers 2502.06530, arXiv.org, revised Mar 2025.
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    17. 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.
    18. Lu Hong & Scott E. Page, 2025. "The range of collective accuracy for binary classifications under majority rule," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 79(1), pages 275-300, February.
    19. 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.
    20. Ichihashi, Shota, 2021. "The economics of data externalities," Journal of Economic Theory, Elsevier, vol. 196(C).
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    22. 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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