IDEAS home Printed from https://ideas.repec.org/p/bdp/wpaper/2014006.html
   My bibliography  Save this paper

Fairness and Efficiency in a Random Assignment: Three Impossibility Results

Author

Listed:
  • Alexander Nesterov

    (Wissenschaftszentrum für Sozialforschung Berlin)

Abstract

This paper considers the problem of allocating N indivisible objects among N agents according to their preferences when transfers are not allowed, and studies the tradeoff between fairness and efficiency in the class of strategy-proof mechanisms. The main finding is that for strategy-proof mechanisms the following efficiency and fairness criteria are mutually incompatible: (1) Ex-post efficiency and envy-freeness, (2) ordinal efficiency and weak envy-freeness and (3) ordinal efficiency and equal division lower bound. Result (1) is the first impossibility result for this setting that uses ex-post efficiency; results (2) and (3) are more relevant for practical implementation than similar results in the literature. In addition, for N = 3 the paper strengthens the characterization result by Bogomolnaia and Moulin (2001): the random serial dictatorship mechanism is the unique strategy-proof, ex-post efficient mechanism that eliminates strict envy between agents with the same preferences. Creation Date: 2014-11-06

Suggested Citation

  • Alexander Nesterov, "undated". "Fairness and Efficiency in a Random Assignment: Three Impossibility Results," BDPEMS Working Papers 2014006, Berlin School of Economics.
    • Handle: RePEc:bdp:wpaper:2014006
    as

    Download full text from publisher

    File URL: https://repec.berlinschoolofeconomics.de/bdp/wpaper/pdf/WP_2014-06_Fairness_and_Efficiency.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Kojima, Fuhito & Manea, Mihai, 2010. "Incentives in the probabilistic serial mechanism," Journal of Economic Theory, Elsevier, vol. 145(1), pages 106-123, January.
    2. Roth, Alvin E. & Sonmez, Tayfun & Utku Unver, M., 2005. "Pairwise kidney exchange," Journal of Economic Theory, Elsevier, vol. 125(2), pages 151-188, December.
    3. Yeon-Koo Che & Fuhito Kojima, 2010. "Asymptotic Equivalence of Probabilistic Serial and Random Priority Mechanisms," Econometrica, Econometric Society, vol. 78(5), pages 1625-1672, September.
    4. Peter Coles & John Cawley & Phillip B. Levine & Muriel Niederle & Alvin E. Roth & John J. Siegfried, 2010. "The Job Market for New Economists: A Market Design Perspective," Journal of Economic Perspectives, American Economic Association, vol. 24(4), pages 187-206, Fall.
    5. Alvin E. Roth & Tayfun Sönmez & M. Utku Ünver, 2004. "Kidney Exchange," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(2), pages 457-488.
    6. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    7. Atila Abdulkadiroglu & Tayfun Sonmez, 1998. "Random Serial Dictatorship and the Core from Random Endowments in House Allocation Problems," Econometrica, Econometric Society, vol. 66(3), pages 689-702, May.
    8. Onur Kesten & Ayşe Yazıcı, 2012. "The Pareto-dominant strategy-proof and fair rule for problems with indivisible goods," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(2), pages 463-488, June.
    9. Erdil, Aytek, 2014. "Strategy-proof stochastic assignment," Journal of Economic Theory, Elsevier, vol. 151(C), pages 146-162.
    10. Horowitz, John K. & McConnell, Kenneth E., 2002. "A Review of WTA/WTP Studies," Journal of Environmental Economics and Management, Elsevier, vol. 44(3), pages 426-447, November.
    11. 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.
    12. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
    13. Aytek Erdil, 2013. "Strategy-Proof Stochastic Assignment," Cambridge Working Papers in Economics 1333, Faculty of Economics, University of Cambridge.
    14. Yan Chen & Tayfun Sönmez, 2002. "Improving Efficiency of On-Campus Housing: An Experimental Study," American Economic Review, American Economic Association, vol. 92(5), pages 1669-1686, December.
    15. Andrea Isoni & Graham Loomes & Robert Sugden, 2011. "The Willingness to Pay—Willingness to Accept Gap, the "Endowment Effect," Subject Misconceptions, and Experimental Procedures for Eliciting Valuations: Comment," American Economic Review, American Economic Association, vol. 101(2), pages 991-1011, April.
    16. Atila Abdulkadiroglu & Yeon-Koo Che & Yosuke Yasuda, 2011. "Resolving Conflicting Preferences in School Choice: The "Boston Mechanism" Reconsidered," American Economic Review, American Economic Association, vol. 101(1), pages 399-410, February.
    17. Hashimoto, Tadashi & Hirata, Daisuke & Kesten, Onur & Kurino, Morimitsu & Unver, Utku, 2014. "Two axiomatic approaches to the probabilistic serial mechanism," Theoretical Economics, Econometric Society, vol. 9(1), January.
    18. William Thomson, 2007. "Fair Allocation Rules," RCER Working Papers 539, University of Rochester - Center for Economic Research (RCER).
    19. 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.
    20. Abdulkadiroglu, Atila & Sonmez, Tayfun, 2003. "Ordinal efficiency and dominated sets of assignments," Journal of Economic Theory, Elsevier, vol. 112(1), pages 157-172, September.
    21. Kesten, Onur, 2009. "Why do popular mechanisms lack efficiency in random environments?," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2209-2226, 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. 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.
    2. Bade, Sophie, 2016. "Fairness and group-strategyproofness clash in assignment problems," Journal of Economic Theory, Elsevier, vol. 165(C), pages 257-262.

    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. Nesterov, Alexander S., 2017. "Fairness and efficiency in strategy-proof object allocation mechanisms," Journal of Economic Theory, Elsevier, vol. 170(C), pages 145-168.
    2. 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.
    3. Shende, Priyanka & Purohit, Manish, 2023. "Strategy-proof and envy-free mechanisms for house allocation," Journal of Economic Theory, Elsevier, vol. 213(C).
    4. Hugh-Jones, David & Kurino, Morimitsu & Vanberg, Christoph, 2014. "An experimental study on the incentives of the probabilistic serial mechanism," Games and Economic Behavior, Elsevier, vol. 87(C), pages 367-380.
    5. Bogomolnaia, Anna & Moulin, Herve, 2015. "Size versus fairness in the assignment problem," Games and Economic Behavior, Elsevier, vol. 90(C), pages 119-127.
    6. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Østerdal, Lars Peter, 2014. "Assigning agents to a line," Games and Economic Behavior, Elsevier, vol. 87(C), pages 539-553.
    7. YIlmaz, Özgür, 2010. "The probabilistic serial mechanism with private endowments," Games and Economic Behavior, Elsevier, vol. 69(2), pages 475-491, July.
    8. Han, Xiang, 2024. "A theory of fair random allocation under priorities," Theoretical Economics, Econometric Society, vol. 19(3), July.
    9. Mennle, Timo & Seuken, Sven, 2021. "Partial strategyproofness: Relaxing strategyproofness for the random assignment problem," Journal of Economic Theory, Elsevier, vol. 191(C).
    10. Anno, Hidekazu & Kurino, Morimitsu, 2016. "On the operation of multiple matching markets," Games and Economic Behavior, Elsevier, vol. 100(C), pages 166-185.
    11. 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.
    12. Ivan Balbuzanov & Maciej H. Kotowski, 2019. "Endowments, Exclusion, and Exchange," Econometrica, Econometric Society, vol. 87(5), pages 1663-1692, September.
    13. Roth, Alvin E. & Sonmez, Tayfun & Utku Unver, M., 2005. "Pairwise kidney exchange," Journal of Economic Theory, Elsevier, vol. 125(2), pages 151-188, December.
    14. Kojima, Fuhito, 2013. "Efficient resource allocation under multi-unit demand," Games and Economic Behavior, Elsevier, vol. 82(C), pages 1-14.
    15. Kesten, Onur & Unver, Utku, 2015. "A theory of school choice lotteries," Theoretical Economics, Econometric Society, vol. 10(2), May.
    16. Chang, Hee-In & Chun, Youngsub, 2017. "Probabilistic assignment of indivisible objects when agents have the same preferences except the ordinal ranking of one object," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 80-92.
    17. Morimitsu Kurino, 2014. "House Allocation with Overlapping Generations," American Economic Journal: Microeconomics, American Economic Association, vol. 6(1), pages 258-289, February.
    18. Kojima, Fuhito & Manea, Mihai, 2010. "Incentives in the probabilistic serial mechanism," Journal of Economic Theory, Elsevier, vol. 145(1), pages 106-123, January.
    19. Jingsheng Yu & Jun Zhang, 2020. "Efficient and fair trading algorithms in market design environments," Papers 2005.06878, arXiv.org, revised May 2021.
    20. Fuhito Kojima & M. Ünver, 2014. "The “Boston” school-choice mechanism: an axiomatic approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 515-544, April.

    More about this item

    Keywords

    random assignment; random serial dictatorship; strategy-proofness; ex-post efficiency; weak envy-freeness; equal division lower bound;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

    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:bdp:wpaper:2014006. 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: Christian Reiter (email available below). General contact details of provider: https://edirc.repec.org/data/bdpemde.html .

    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.