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When are signals complements or substitutes?

Author

Listed:
  • Börgers, Tilman
  • Hernando-Veciana, Ángel
  • 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 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

  • Börgers, Tilman & Hernando-Veciana, Ángel & 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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    Cited by:

    1. Pierre Chaigneau & Nicolas Sahuguet, 2023. "The Complementarity Between Signal Informativeness and Monitoring," Journal of Accounting Research, John Wiley & Sons, Ltd., vol. 61(1), pages 141-185, March.
    2. James Andreoni & Tymofiy Mylovanov, 2012. "Diverging Opinions," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 209-232, February.
    3. Kambhampati, Ashwin & Segura-Rodriguez, Carlos & Shao, Peng, 2024. "Why informationally diverse teams need not form, even when efficient," Journal of Economic Behavior & Organization, Elsevier, vol. 226(C).
    4. 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.
    5. Federico Vaccari, 2024. "Belief patterns with information processing," Papers 2411.17597, arXiv.org.
    6. Kaya, Ayça & Vereshchagina, Galina, 2022. "Sorting expertise," Journal of Economic Theory, Elsevier, vol. 204(C).
    7. Chade, Hector & Eeckhout, Jan, 2018. "Matching information," Theoretical Economics, Econometric Society, vol. 13(1), January.
    8. Deniz Kattwinkel & Axel Niemeyer & Justus Preusser & Alexander Winter, 2022. "Mechanisms without transfers for fully biased agents," Papers 2205.10910, arXiv.org.
    9. Mark Whitmeyer & Cole Williams, 2024. "Dynamic Signals," Papers 2407.16648, arXiv.org.
    10. Francesco Sangiorgi & Chester Spatt, 2017. "Opacity, Credit Rating Shopping, and Bias," Management Science, INFORMS, vol. 63(12), pages 4016-4036, December.
    11. Peter Achim & Roland Strausz, 2025. "Oligopolistic Information Markets," Rationality and Competition Discussion Paper Series 554, CRC TRR 190 Rationality and Competition.
    12. Jean-Sauveur Ay & Julie Le Gallo, 2021. "The signaling value of nested wine names," Post-Print hal-03268014, HAL.
    13. Bergemann, Dirk & Ottaviani, Marco, 2021. "Information Markets and Nonmarkets," CEPR Discussion Papers 16459, C.E.P.R. Discussion Papers.
    14. ,, 2014. "On the relationship between individual and group decisions," Theoretical Economics, Econometric Society, vol. 9(1), January.
    15. Jan Knoepfle, 2024. "Dynamic Competition for Attention," Papers 2409.18595, arXiv.org, revised Oct 2024.
    16. Kailin Chen, 2025. "Ranking Statistical Experiments via the Linear Convex Order and the Lorenz Zonoid: Economic Applications," Papers 2502.06530, arXiv.org, revised Feb 2026.
    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. Roland Strausz, 2024. "Correlation‐savvy sellers," RAND Journal of Economics, RAND Corporation, vol. 55(2), pages 266-291, June.
    19. 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.
    20. 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.
    21. Ichihashi, Shota, 2021. "The economics of data externalities," Journal of Economic Theory, Elsevier, vol. 196(C).
    22. Joel Sobel, 2014. "On the relationship between individual and group decisions," Levine's Working Paper Archive 786969000000000950, David K. Levine.
    23. 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.

    More about this item

    Keywords

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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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