IDEAS home Printed from https://ideas.repec.org/p/cte/werepe/we072111.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: https://e-archivo.uc3m.es/rest/api/core/bitstreams/5abc7816-d334-46bc-88d8-52b935b960dc/content
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    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. Nicola Persico, 2000. "Information Acquisition in Auctions," Econometrica, Econometric Society, vol. 68(1), pages 135-148, January.
    4. 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.
    5. Efe A. Ok, 2007. "Preliminaries of Real Analysis, from Real Analysis with Economic Applications," Introductory Chapters, in: Real Analysis with Economic Applications, Princeton University Press.
    6. Athey, Susan & Levin, Jonathan, 2018. "The value of information in monotone decision problems," Research in Economics, Elsevier, vol. 72(1), pages 101-116.
    7. James Andreoni & Tymofiy Mylovanov, 2012. "Diverging Opinions," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 209-232, February.
    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. McLennan, Andrew, 1998. "Consequences of the Condorcet Jury Theorem for Beneficial Information Aggregation by Rational Agents," American Political Science Review, Cambridge University Press, vol. 92(2), pages 413-418, June.
    10. 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.
    11. Miklos Sarvary & Philip M. Parker, 1997. "Marketing Information: A Competitive Analysis," Marketing Science, INFORMS, vol. 16(1), pages 24-38.
    12. Nicola Persico, 2004. "Committee Design with Endogenous Information," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(1), pages 165-191.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Dirk Bergemann & Marco Ottaviani, 2021. "Information Markets and Nonmarkets," Cowles Foundation Discussion Papers 2296, Cowles Foundation for Research in Economics, Yale University.
    2. Chade, Hector & Eeckhout, Jan, 2018. "Matching information," Theoretical Economics, Econometric Society, vol. 13(1), January.
    3. Mira Frick & Ryota Iijima & Yuhta Ishii, 2021. "Learning Efficiency of Multi-Agent Information Structures," Cowles Foundation Discussion Papers 2299R, Cowles Foundation for Research in Economics, Yale University, revised Dec 2021.
    4. Pierre Chaigneau & Nicolas Sahuguet, 2023. "The Complementarity Between Signal Informativeness and Monitoring," Journal of Accounting Research, Wiley Blackwell, vol. 61(1), pages 141-185, March.
    5. James Andreoni & Tymofiy Mylovanov, 2012. "Diverging Opinions," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 209-232, February.
    6. ,, 2014. "On the relationship between individual and group decisions," Theoretical Economics, Econometric Society, vol. 9(1), January.
    7. Jan Knoepfle, 2024. "Dynamic Competition for Attention," Papers 2409.18595, arXiv.org, revised Oct 2024.
    8. Jean-Sauveur Ay & Julie Le Gallo, 2021. "The signaling value of nested wine names," Post-Print hal-03268014, HAL.
    9. Roland Strausz, 2024. "Correlation‐savvy sellers," RAND Journal of Economics, RAND Corporation, vol. 55(2), pages 266-291, June.
    10. 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.
    11. Mark Whitmeyer & Cole Williams, 2024. "Dynamic Signals," Papers 2407.16648, arXiv.org.
    12. 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.
    13. Kaya, Ayça & Vereshchagina, Galina, 2022. "Sorting expertise," Journal of Economic Theory, Elsevier, vol. 204(C).
    14. Francesco Sangiorgi & Chester Spatt, 2017. "Opacity, Credit Rating Shopping, and Bias," Management Science, INFORMS, vol. 63(12), pages 4016-4036, December.
    15. Ichihashi, Shota, 2021. "The economics of data externalities," Journal of Economic Theory, Elsevier, vol. 196(C).
    16. Deniz Kattwinkel & Axel Niemeyer & Justus Preusser & Alexander Winter, 2022. "Mechanisms without transfers for fully biased agents," Papers 2205.10910, arXiv.org.
    17. Joel Sobel, 2014. "On the relationship between individual and group decisions," Levine's Working Paper Archive 786969000000000950, David K. Levine.
    18. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gershkov, Alex & Szentes, Balázs, 2009. "Optimal voting schemes with costly information acquisition," Journal of Economic Theory, Elsevier, vol. 144(1), pages 36-68, January.
    2. de Clippel, Geoffroy & Eliaz, Kfir, 2015. "Premise-based versus outcome-based information aggregation," Games and Economic Behavior, Elsevier, vol. 89(C), pages 34-42.
    3. Cesar Martinelli, 2011. "Ignorance and Naivete in Large Elections," Working Papers 1107, Centro de Investigacion Economica, ITAM.
    4. Irem Bozbay, 2019. "Truth-tracking judgment aggregation over interconnected issues," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(2), pages 337-370, August.
    5. Jerome Mathis, 2006. "Deliberation with Partially Verifiable Information," THEMA Working Papers 2006-03, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    6. Paolo Balduzzi & Clara Graziano & Annalisa Luporini, 2014. "Voting in small committees," Journal of Economics, Springer, vol. 111(1), pages 69-95, February.
    7. Hernando-Veciana, Ángel, 2009. "Information acquisition in auctions: Sealed bids vs. open bids," Games and Economic Behavior, Elsevier, vol. 65(2), pages 372-405, March.
    8. Bozbay, Irem & Peters, Hans, 2019. "Information aggregation with a continuum of types," Economics Letters, Elsevier, vol. 180(C), pages 46-49.
    9. Elisabeth Schulte, 2010. "Information aggregation and preference heterogeneity in committees," Theory and Decision, Springer, vol. 69(1), pages 97-118, July.
    10. Laurent Bouton & Aniol Llorente-Saguer & Antonin Macé & Dimitrios Xefteris, 2021. "Voting Rights, Agenda Control and Information Aggregation," NBER Working Papers 29005, National Bureau of Economic Research, Inc.
    11. Ruth Ben-Yashar & Igal Milchtaich, 2003. "First and Second Best Voting Rules in Committees," Working Papers 2003-08, Bar-Ilan University, Department of Economics.
    12. Laurent Bouton & Aniol Llorente-Saguer & Frédéric Malherbe, 2014. "Get Rid of Unanimity: The Superiority of Majority Rule with Veto Power," NBER Working Papers 20417, National Bureau of Economic Research, Inc.
    13. Bouton, Laurent & Llorente-Saguer, Aniol & Malherbe, Frédéric, 2017. "Unanimous rules in the laboratory," Games and Economic Behavior, Elsevier, vol. 102(C), pages 179-198.
    14. Bouton, Laurent & Castanheira, Micael & Llorente-Saguer, Aniol, 2016. "Divided majority and information aggregation: Theory and experiment," Journal of Public Economics, Elsevier, vol. 134(C), pages 114-128.
    15. Irem Bozbay, 2015. "Truth-Tracking Judgment Aggregation Over Interconnected Issues," School of Economics Discussion Papers 0916, School of Economics, University of Surrey.
    16. Vasilis Syrgkanis & David Kempe & Eva Tardos, 2019. "Information Asymmetries in Common-Value Auctions with Discrete Signals," Management Science, INFORMS, vol. 44(4), pages 1450-1476, November.
    17. Sourav Bhattacharya, 2006. "Preference Monotonicity and Information Aggregation in Elections," Working Paper 325, Department of Economics, University of Pittsburgh, revised Dec 2008.
    18. Philip Bond & Hülya Eraslan, 2004. "Strategic Voting over Strategic Proposals, Second Version," PIER Working Paper Archive 07-014, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 02 Jan 2007.
    19. Martinelli, Cesar, 2006. "Would rational voters acquire costly information?," Journal of Economic Theory, Elsevier, vol. 129(1), pages 225-251, July.
    20. Laurent Bouto & Aniol Llorente-Saguer & Fédéric Malherbe, 2014. "Get Rid of Unanimity: The Superiority of Majority Rule with Veto Power," Working Papers 722, Queen Mary University of London, School of Economics and Finance.

    More about this item

    Keywords

    Complementarity;

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cte:werepe:we072111. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ana Poveda (email available below). General contact details of provider: http://www.eco.uc3m.es/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.