IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v168y2017icp1-11.html
   My bibliography  Save this article

Ordinal aggregation results via Karlin's variation diminishing property

Author

Listed:
  • Choi, Michael
  • Smith, Lones

Abstract

When is the weighted sum of quasi-concave functions quasi-concave? We answer this, extending an analogous preservation of the single-crossing property in QS: Quah and Strulovici (2012). Our approach develops a general preservation of n-crossing properties, applying the variation diminishing property in Karlin (1956). The QS premise is equivalent to Karlin's total positivity of order two, while our premise uses total positivity of order three: The weighted sum of quasi-concave functions is quasi-concave if each has an increasing portion more risk averse than any decreasing portion.

Suggested Citation

  • Choi, Michael & Smith, Lones, 2017. "Ordinal aggregation results via Karlin's variation diminishing property," Journal of Economic Theory, Elsevier, vol. 168(C), pages 1-11.
    • Handle: RePEc:eee:jetheo:v:168:y:2017:i:c:p:1-11
    DOI: 10.1016/j.jet.2016.12.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053116301107
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2016.12.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jewitt, Ian, 1988. "Justifying the First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 56(5), pages 1177-1190, September.
    2. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    3. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    4. John K.‐H. Quah & Bruno Strulovici, 2012. "Aggregating the Single Crossing Property," Econometrica, Econometric Society, vol. 80(5), pages 2333-2348, September.
    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. Anton Kolotilin & Alexander Wolitzky, 2020. "Assortative Information Disclosure," Discussion Papers 2020-08, School of Economics, The University of New South Wales.
    2. Liu, Shuo & Pei, Harry, 2020. "Monotone equilibria in signaling games," European Economic Review, Elsevier, vol. 124(C).
    3. Anton Kolotilin & Roberto Corrao & Alexander Wolitzky, 2022. "Persuasion with Non-Linear Preferences," Papers 2206.09164, arXiv.org, revised Aug 2022.
    4. Barthel, Anne-Christine & Hoffmann, Eric & Sabarwal, Tarun, 2022. "Characterizing robust solutions in monotone games," Games and Economic Behavior, Elsevier, vol. 135(C), pages 201-219.
    5. Anne-Christine Barthel & Eric Hoffmann & Tarun Sabarwal, 2021. "A Unified Approach to p-Dominance and its Generalizations in Games with Strategic Complements and Substitutes," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202109, University of Kansas, Department of Economics.
    6. Shuo Liu & Harry Pei, 2017. "Monotone equilibria in signalling games," ECON - Working Papers 252, Department of Economics - University of Zurich.
    7. Marilyn Pease & Mark Whitmeyer, 2024. "How to Make an Action Better," Papers 2408.09294, arXiv.org, revised Nov 2024.
    8. Hector Chade & Jeroen Swinkels, 2021. "Screening in Vertical Oligopolies," Econometrica, Econometric Society, vol. 89(3), pages 1265-1311, May.

    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. Jewitt, Ian & Mukerji, Sujoy, 2017. "Ordering ambiguous acts," Journal of Economic Theory, Elsevier, vol. 171(C), pages 213-267.
    2. Prokopovych, Pavlo & Yannelis, Nicholas C., 2017. "On strategic complementarities in discontinuous games with totally ordered strategies," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 147-153.
    3. Prokopovych, Pavlo & Yannelis, Nicholas C., 2023. "On monotone pure-strategy Bayesian-Nash equilibria of a generalized contest," Games and Economic Behavior, Elsevier, vol. 140(C), pages 348-362.
    4. Prokopovych, Pavlo & Yannelis, Nicholas C., 2019. "On monotone approximate and exact equilibria of an asymmetric first-price auction with affiliated private information," Journal of Economic Theory, Elsevier, vol. 184(C).
    5. Kunimoto, Takashi & Yamashita, Takuro, 2020. "Order on types based on monotone comparative statics," Journal of Economic Theory, Elsevier, vol. 189(C).
    6. Balbus, Lukasz & Dziewulski, Pawel & Reffett, Kevin & Wozny, Lukasz, 2022. "Markov distributional equilibrium dynamics in games with complementarities and no aggregate risk," Theoretical Economics, Econometric Society, vol. 17(2), May.
    7. Łukasz Balbus & Paweł Dziewulski & Kevin Reffett & Łukasz Woźny, 2015. "Differential information in large games with strategic complementarities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 201-243, May.
    8. Burkhard C. Schipper, 2021. "The evolutionary stability of optimism, pessimism, and complete ignorance," Theory and Decision, Springer, vol. 90(3), pages 417-454, May.
    9. Amir, Rabah & De Castro, Luciano, 2017. "Nash equilibrium in games with quasi-monotonic best-responses," Journal of Economic Theory, Elsevier, vol. 172(C), pages 220-246.
    10. Alain Chateauneuf & Vassili Vergopoulos & Jianbo Zhang, 2018. "Infinite Supermodularity and Preferences," Chapters, in: Danijela Tuljak-Suban (ed.), Game Theory - Applications in Logistics and Economy, IntechOpen.
    11. Patrick Legros & Andrew F. Newman, 2007. "Beauty Is a Beast, Frog Is a Prince: Assortative Matching with Nontransferabilities," Econometrica, Econometric Society, vol. 75(4), pages 1073-1102, July.
    12. Navin Kartik & SangMok Lee & Daniel Rappoport, 2022. "Single-Crossing Differences in Convex Environments," Papers 2212.12009, arXiv.org, revised Jun 2023.
    13. Axel Anderson & Lones Smith, 2024. "The Comparative Statics of Sorting," American Economic Review, American Economic Association, vol. 114(3), pages 709-751, March.
    14. Anton Kolotilin & Roberto Corrao & Alexander Wolitzky, 2022. "Persuasion with Non-Linear Preferences," Papers 2206.09164, arXiv.org, revised Aug 2022.
    15. Pavlo Prokopovych & Nicholas C. Yannelis, 2022. "On nondegenerate equilibria of double auctions with several buyers and a price floor," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 625-654, April.
    16. Yang, Jian, 2018. "Game-theoretic modeling of players’ ambiguities on external factors," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 31-56.
    17. Wang, Jianli & Li, Jingyuan, 2016. "Lattice-based monotone comparative statics on saving with Selden/Kreps–Porteus preferences," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 132-138.
    18. Starkov, Egor, 2023. "Only time will tell: Credible dynamic signaling," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    19. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    20. Łukasz Balbus & Paweł Dziewulski & Kevin Reffett & Łukasz Woźny, 2019. "A qualitative theory of large games with strategic complementarities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 497-523, April.

    More about this item

    Keywords

    Single-crossing property; Quasi-concavity; Variation diminishing property; Logsupermodularity; Signed-ratio monotonicity;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

    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:eee:jetheo:v:168:y:2017:i:c:p:1-11. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    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.