IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v193y2021ics0022053121000247.html
   My bibliography  Save this article

On the existence of Pareto Efficient and envy-free allocations

Author

Listed:
  • Cole, Richard
  • Tao, Yixin

Abstract

Envy-freeness and Pareto Efficiency are two major goals in welfare economics. The existence of an allocation that satisfies both conditions has been studied for a long time. Whether items are indivisible or divisible, it is impossible to achieve envy-freeness and Pareto Efficiency ex post even in the case of two people and two items. In contrast, in this work, we prove that, for any cardinal utility functions (including complementary utilities for example) and for any number of items and players, there always exists an ex ante mixed allocation which is envy-free and Pareto Efficient, assuming the allowable assignments satisfy an anonymity property. The problem remains open in the divisible case.

Suggested Citation

  • Cole, Richard & Tao, Yixin, 2021. "On the existence of Pareto Efficient and envy-free allocations," Journal of Economic Theory, Elsevier, vol. 193(C).
    • Handle: RePEc:eee:jetheo:v:193:y:2021:i:c:s0022053121000247
    DOI: 10.1016/j.jet.2021.105207
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053121000247
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2021.105207?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. Varian, Hal R., 1974. "Equity, envy, and efficiency," Journal of Economic Theory, Elsevier, vol. 9(1), pages 63-91, September.
    2. Richter, Michael & Rubinstein, Ariel, 2020. "The permissible and the forbidden," Journal of Economic Theory, Elsevier, vol. 188(C).
    3. Hylland, Aanund & Zeckhauser, Richard, 1979. "The Efficient Allocation of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 87(2), pages 293-314, April.
    4. Eric Budish & Yeon-Koo Che & Fuhito Kojima & Paul Milgrom, 2013. "Designing Random Allocation Mechanisms: Theory and Applications," American Economic Review, American Economic Association, vol. 103(2), pages 585-623, April.
    5. Herve Moulin, 2004. "Fair Division and Collective Welfare," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633116, December.
    6. Maniquet, Francois, 1999. "A strong incompatibility between efficiency and equity in non-convex economies," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 467-474, December.
    7. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
    8. Eric Budish, 2011. "The Combinatorial Assignment Problem: Approximate Competitive Equilibrium from Equal Incomes," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1061-1103.
    9. Kaneko, Mamoru & Nakamura, Kenjiro, 1979. "The Nash Social Welfare Function," Econometrica, Econometric Society, vol. 47(2), pages 423-435, March.
    10. Goldberg, Paul W. & Pastink, Arnoud, 2014. "On the communication complexity of approximate Nash equilibria," Games and Economic Behavior, Elsevier, vol. 85(C), pages 19-31.
    11. Weller, Dietrich, 1985. "Fair division of a measurable space," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 5-17, February.
    12. Nisan, Noam & Segal, Ilya, 2006. "The communication requirements of efficient allocations and supporting prices," Journal of Economic Theory, Elsevier, vol. 129(1), pages 192-224, July.
    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. Guy Barokas, 2022. "Revealed desirability: a novel instrument for social welfare," Theory and Decision, Springer, vol. 93(4), pages 649-661, November.

    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. Ortega, Josué, 2020. "Multi-unit assignment under dichotomous preferences," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 15-24.
    2. He, Yinghua & Li, Sanxi & Yan, Jianye, 2015. "Evaluating assignment without transfers: A market perspective," Economics Letters, Elsevier, vol. 133(C), pages 40-44.
    3. Scott Duke Kominers & Alexander Teytelboym & Vincent P Crawford, 2017. "An invitation to market design," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 33(4), pages 541-571.
    4. Miralles, Antonio & Pycia, Marek, 2021. "Foundations of pseudomarkets: Walrasian equilibria for discrete resources," Journal of Economic Theory, Elsevier, vol. 196(C).
    5. Eun Jeong Heo & Vikram Manjunath, 2017. "Implementation in stochastic dominance Nash equilibria," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 5-30, January.
    6. Zhan Wang & Jinpeng Ma & Hongwei Zhang, 2023. "Object-based unawareness: Theory and applications," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 8(1), pages 1-55, December.
    7. Onur Kesten & Morimitsu Kurino & Alexander S. Nesterov, 2017. "Efficient lottery design," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 31-57, January.
    8. Nikhil Agarwal & Eric Budish, 2021. "Market Design," NBER Working Papers 29367, National Bureau of Economic Research, Inc.
    9. Nguyen, Thành & Peivandi, Ahmad & Vohra, Rakesh, 2016. "Assignment problems with complementarities," Journal of Economic Theory, Elsevier, vol. 165(C), pages 209-241.
    10. Chatterji, Shurojit & Liu, Peng, 2020. "Random assignments of bundles," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 15-30.
    11. Federico Echenique & Antonio Miralles & Jun Zhang, 2019. "Fairness and efficiency for probabilistic allocations with participation constraints," Papers 1908.04336, arXiv.org, revised May 2020.
    12. Hashimoto, Tadashi, 2018. "The generalized random priority mechanism with budgets," Journal of Economic Theory, Elsevier, vol. 177(C), pages 708-733.
    13. Georgios Gerasimou, 2019. "Simple Preference Intensity Comparisons," Discussion Paper Series, School of Economics and Finance 201905, School of Economics and Finance, University of St Andrews, revised 27 Apr 2020.
    14. Thanh Nguyen & Ahmad Peivandi & Rakesh Vohra, 2014. "One-Sided Matching with Limited Complementarities," PIER Working Paper Archive 14-030, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    15. Yinghua He & Antonio Miralles & Marek Pycia & Jianye Yan, 2018. "A Pseudo-Market Approach to Allocation with Priorities," American Economic Journal: Microeconomics, American Economic Association, vol. 10(3), pages 272-314, August.
    16. Thomson, William, 2011. "Chapter Twenty-One - Fair Allocation Rules," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 2, chapter 21, pages 393-506, Elsevier.
    17. Echenique, Federico & Miralles, Antonio & Zhang, Jun, 2021. "Fairness and efficiency for allocations with participation constraints," Journal of Economic Theory, Elsevier, vol. 195(C).
    18. Balbuzanov, Ivan, 2022. "Constrained random matching," Journal of Economic Theory, Elsevier, vol. 203(C).
    19. Ioannis Caragiannis & David Kurokawa & Herve Moulin & Ariel D. Procaccia & Nisarg Shah & Junxing Wang, 2016. "The Unreasonable Fairness of Maximum Nash Welfare," Working Papers 2016_08, Business School - Economics, University of Glasgow.
    20. Haris Aziz & Yoichi Kasajima, 2017. "Impossibilities for probabilistic assignment," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(2), pages 255-275, August.

    More about this item

    Keywords

    Pareto Efficient; Envy-free; Fair allocation; Communication complexity;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis

    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:193:y:2021:i:c:s0022053121000247. 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.