IDEAS home Printed from https://ideas.repec.org/p/bon/boncrc/crctr224_2021_288.html
   My bibliography  Save this paper

Extreme Points and Majorization: Economic Applications

Author

Listed:
  • Andreas Kleiner
  • Benny Moldovanu
  • Philipp Strack

Abstract

We characterize the set of extreme points of monotonic functions that are either majorized by a given function f or themselves majorize f and show that these extreme points play a crucial role in many economic design problems. Our main results show that each extreme point is uniquely characterized by a countable collection of intervals. Outside these intervals the extreme point equals the original function f and inside the function is constant. Further consistency conditions need to be satisfied pinning down the value of an extreme point in each interval where it is constant. We apply these insights to a varied set of economic problems: equivalence and optimality of mechanisms for auctions and (matching) contests, Bayesian persuasion, optimal delegation, and decision making under uncertainty.

Suggested Citation

  • Andreas Kleiner & Benny Moldovanu & Philipp Strack, 2021. "Extreme Points and Majorization: Economic Applications," CRC TR 224 Discussion Paper Series crctr224_2021_288, University of Bonn and University of Mannheim, Germany.
    • Handle: RePEc:bon:boncrc:crctr224_2021_288
    as

    Download full text from publisher

    File URL: https://www.crctr224.de/research/discussion-papers/archive/dp288
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Sergiu Hart & Philip J. Reny, 2015. "Implementation of reduced form mechanisms: a simple approach and a new characterization," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 1-8, April.
    2. Anton Kolotilin & Andriy Zapechelnyuk, 2018. "Persuasion Meets Delegation," Discussion Papers 2018-06, School of Economics, The University of New South Wales.
    3. Alexey Kushnir, 2013. "On the equivalence between Bayesian and dominant strategy implementation: the case of correlated types," ECON - Working Papers 129, Department of Economics - University of Zurich.
    4. Ettore Damiano & Hao Li, 2007. "Price discrimination and efficient matching," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(2), pages 243-263, February.
    5. Heidrun C. Hoppe & Benny Moldovanu & Aner Sela, 2009. "The Theory of Assortative Matching Based on Costly Signals," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(1), pages 253-281.
    6. Navin Kartik & Andreas Kleiner & Richard Van Weelden, 2021. "Delegation in Veto Bargaining," American Economic Review, American Economic Association, vol. 111(12), pages 4046-4087, December.
    7. Kolotilin, Anton, 2018. "Optimal information disclosure: a linear programming approach," Theoretical Economics, Econometric Society, vol. 13(2), May.
    8. Piotr Dworczak & Giorgio Martini, 2019. "The Simple Economics of Optimal Persuasion," Journal of Political Economy, University of Chicago Press, vol. 127(5), pages 1993-2048.
    9. Toikka, Juuso, 2011. "Ironing without control," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2510-2526.
    10. Matthews, Steven A, 1984. "On the Implementability of Reduced Form Auctions," Econometrica, Econometric Society, vol. 52(6), pages 1519-1522, November.
    11. Border, Kim C, 1991. "Implementation of Reduced Form Auctions: A Geometric Approach," Econometrica, Econometric Society, vol. 59(4), pages 1175-1187, July.
    12. Andreas Kleiner & Benny Moldovanu & Philipp Strack, 2021. "Extreme Points and Majorization: Economic Applications," Econometrica, Econometric Society, vol. 89(4), pages 1557-1593, July.
    13. Gershkov, Alex & Moldovanu, Benny, 2010. "Efficient sequential assignment with incomplete information," Games and Economic Behavior, Elsevier, vol. 68(1), pages 144-154, January.
    14. Dizdar, Deniz & Kováč, Eugen, 2020. "A simple proof of strong duality in the linear persuasion problem," Games and Economic Behavior, Elsevier, vol. 122(C), pages 407-412.
    15. Alex Gershkov & Jacob K. Goeree & Alexey Kushnir & Benny Moldovanu & Xianwen Shi, 2013. "On the Equivalence of Bayesian and Dominant Strategy Implementation," Econometrica, Econometric Society, vol. 81(1), pages 197-220, January.
    16. Yeon‐Koo Che & Jinwoo Kim & Konrad Mierendorff, 2013. "Generalized Reduced‐Form Auctions: A Network‐Flow Approach," Econometrica, Econometric Society, vol. 81(6), pages 2487-2520, November.
    17. Kovác, Eugen & Mylovanov, Tymofiy, 2009. "Stochastic mechanisms in settings without monetary transfers: The regular case," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1373-1395, July.
    18. Manuel Amador & Kyle Bagwell, 2013. "The Theory of Optimal Delegation With an Application to Tariff Caps," Econometrica, Econometric Society, vol. 81(4), pages 1541-1599, July.
    19. Condorelli, Daniele, 2012. "What money canʼt buy: Efficient mechanism design with costly signals," Games and Economic Behavior, Elsevier, vol. 75(2), pages 613-624.
    20. Alejandro M. Manelli & Daniel R. Vincent, 2010. "Bayesian and Dominant‐Strategy Implementation in the Independent Private‐Values Model," Econometrica, Econometric Society, vol. 78(6), pages 1905-1938, November.
    21. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    22. Jacob K. Goeree & Alexey Kushnir, 2011. "A geometric approach to mechanism design," ECON - Working Papers 056, Department of Economics - University of Zurich, revised Jun 2013.
    23. Gerhard Winkler, 1988. "Extreme Points of Moment Sets," Mathematics of Operations Research, INFORMS, vol. 13(4), pages 581-587, November.
    24. Kala Krishna & Sergey Lychagin & Wojciech Olszewski & Ron Siegel & Chloe Tergiman, 2022. "Pareto Improvements in the Contest for College Admissions," NBER Working Papers 30220, National Bureau of Economic Research, Inc.
    25. Maryam Saeedi & Ali Shourideh, 2020. "Optimal Rating Design under Moral Hazard," Papers 2008.09529, arXiv.org, revised Jul 2023.
    26. Nahum D. Melumad & Toshiyuki Shibano, 1991. "Communication in Settings with No. Transfers," RAND Journal of Economics, The RAND Corporation, vol. 22(2), pages 173-198, Summer.
    Full references (including those not matched with items on IDEAS)

    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. Goeree, Jacob K. & Kushnir, Alexey, 2016. "Reduced form implementation for environments with value interdependencies," Games and Economic Behavior, Elsevier, vol. 99(C), pages 250-256.
    2. Alex Gershkov & Benny Moldovanu & Philipp Strack & Mengxi Zhang, 2021. "A Theory of Auctions with Endogenous Valuations," Journal of Political Economy, University of Chicago Press, vol. 129(4), pages 1011-1051.
    3. Xu Lang & Zaifu Yang, 2023. "Reduced-Form Allocations for Multiple Indivisible Objects under Constraints," Discussion Papers 23/02, Department of Economics, University of York.
    4. Xu Lang & Zaifu Yang, 2021. "Reduced-Form Allocations for Multiple Indivisible Objects under Constraints: A Revision," Discussion Papers 21/05, Department of Economics, University of York.
    5. Xu Lang, 2023. "A Belief-Based Characterization of Reduced-Form Auctions," Papers 2307.04070, arXiv.org.
    6. Xu Lang, 2022. "Reduced-Form Allocations with Complementarity: A 2-Person Case," Papers 2202.06245, arXiv.org, revised Feb 2022.
    7. Erya Yang, 2021. "Reduced-form mechanism design and ex post fairness constraints," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 269-293, October.
    8. Xu Lang, 2022. "Reduced-form budget allocation with multiple public alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(2), pages 335-359, August.
    9. Xu Lang & Zaifu Yang, 2021. "Reduced-Form Allocations for Multiple Indivisible Objects under Constraints," Discussion Papers 21/04, Department of Economics, University of York.
    10. Mohammad Akbarpour & Piotr Dworczak & Scott Duke Kominers, 2024. "Redistributive Allocation Mechanisms," Journal of Political Economy, University of Chicago Press, vol. 132(6), pages 1831-1875.
    11. Sergiu Hart & Philip J. Reny, 2015. "Implementation of reduced form mechanisms: a simple approach and a new characterization," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 1-8, April.
    12. Maxim Ivanov, 2021. "Optimal monotone signals in Bayesian persuasion mechanisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(3), pages 955-1000, October.
    13. Kolotilin, Anton & Li, Hongyi, 2021. "Relational communication," Theoretical Economics, Econometric Society, vol. 16(4), November.
    14. Andreas Kleiner, 2022. "Optimal Delegation in a Multidimensional World," Papers 2208.11835, arXiv.org.
    15. Piotr Dworczak, 2020. "Mechanism Design With Aftermarkets: Cutoff Mechanisms," Econometrica, Econometric Society, vol. 88(6), pages 2629-2661, November.
    16. Alexander V. Kolesnikov & Fedor Sandomirskiy & Aleh Tsyvinski & Alexander P. Zimin, 2022. "Beckmann's approach to multi-item multi-bidder auctions," Papers 2203.06837, arXiv.org, revised Sep 2022.
    17. Drexl, Moritz & Kleiner, Andreas, 2015. "Optimal private good allocation: The case for a balanced budget," Games and Economic Behavior, Elsevier, vol. 94(C), pages 169-181.
    18. Li, Yunan, 2019. "Efficient mechanisms with information acquisition," Journal of Economic Theory, Elsevier, vol. 182(C), pages 279-328.
    19. Anton Kolotilin & Andriy Zapechelnyuk, 2018. "Persuasion Meets Delegation," Discussion Papers 2018-06, School of Economics, The University of New South Wales.
    20. Tomoya Kazumura & Debasis Mishra & Shigehiro Serizawa, 2017. "Strategy-proof multi-object auction design: Ex-post revenue maximization with no wastage," ISER Discussion Paper 1001, Institute of Social and Economic Research, Osaka University.

    More about this item

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:bon:boncrc:crctr224_2021_288. 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: CRC Office (email available below). General contact details of provider: https://www.crctr224.de .

    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.