IDEAS home Printed from
   My bibliography  Save this paper

Complexity of finding Pareto-efficient allocations of highest welfare


  • Peter Biro

    () (Centre for Economic and Regional Studies and Department of Operations Research and Actuarial Sciences, Corvinus University ofBudapest, Hungary)

  • Jens Gudmundsson

    (Department of Food and Resource Economics, University of Copenhagen, Denmark,)


We allocate objects to agents as exemplified primarily by school choice. Welfare judgments of the object-allocating agency are encoded as edge weights in the acceptability graph. The welfare of an allocation is the sum of its edge weights. We introduce the constrained welfare-maximizing solution, which is the allocation of highest welfare among the Pareto-efficient allocations. We identify conditions under which this solution is easily determined from a computational point of view. For the unrestricted case, we formulate an integer program and find this to be viable in practice as it quickly solves a real-world instance of kindergarten allocation and large-scale simulated instances. Incentives to report preferences truthfully are discussed briefly.

Suggested Citation

  • Peter Biro & Jens Gudmundsson, 2020. "Complexity of finding Pareto-efficient allocations of highest welfare," CERS-IE WORKING PAPERS 2016, Institute of Economics, Centre for Economic and Regional Studies.
  • Handle: RePEc:has:discpr:2016

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth, 2005. "The New York City High School Match," American Economic Review, American Economic Association, vol. 95(2), pages 364-367, May.
    2. Fernández-Huertas Moraga, Jesús & Rapoport, Hillel, 2014. "Tradable immigration quotas," Journal of Public Economics, Elsevier, vol. 115(C), pages 94-108.
    3. ., 2017. "Modification and matching," Chapters, in: An Autecological Theory of the Firm and its Environment, chapter 4, Edward Elgar Publishing.
    4. Eduardo M Azevedo & Eric Budish, 2019. "Strategy-proofness in the Large," Review of Economic Studies, Oxford University Press, vol. 86(1), pages 81-116.
    5. Thomas Sargent & Lars Ljungqvist & Isaac Baley, 2017. "Turbulence and Unemployment in Matching Models," 2017 Meeting Papers 1391, Society for Economic Dynamics.
    6. 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.
    7. Chen, Yan & Sonmez, Tayfun, 2006. "School choice: an experimental study," Journal of Economic Theory, Elsevier, vol. 127(1), pages 202-231, March.
    8. Shengwu Li, 2017. "Obviously Strategy-Proof Mechanisms," American Economic Review, American Economic Association, vol. 107(11), pages 3257-3287, November.
    9. Atila Abdulkadiroglu & Yeon-Koo Che & Parag A. Pathak & Alvin E. Roth & Olivier Tercieux, 2017. "Minimizing Justified Envy in School Choice: The Design of New Orleans' OneApp," NBER Working Papers 23265, National Bureau of Economic Research, Inc.
    10. Roth, Alvin E, 1986. "On the Allocation of Residents to Rural Hospitals: A General Property of Two-Sided Matching Markets," Econometrica, Econometric Society, vol. 54(2), pages 425-427, March.
    11. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    12. 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.
    13. Orhan Aygün & Bertan Turhan, 2017. "Large-Scale Affirmative Action in School Choice: Admissions to IITs in India," American Economic Review, American Economic Association, vol. 107(5), pages 210-213, May.
    14. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    15. Fernández-Huertas Moraga, Jesús & Rapoport, Hillel, 2014. "Tradable immigration quotas," Journal of Public Economics, Elsevier, vol. 115(C), pages 94-108.
    16. Itai Ashlagi & Peng Shi, 2016. "Optimal Allocation Without Money: An Engineering Approach," Management Science, INFORMS, vol. 62(4), pages 1078-1097, April.
    17. Alpern, Steve & Katrantzi, Ioanna, 2009. "Equilibria of two-sided matching games with common preferences," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1214-1222, August.
    18. Roth, Alvin E. & Postlewaite, Andrew, 1977. "Weak versus strong domination in a market with indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 131-137, August.
    19. André Veski & Péter Biró & Kaire Põder & Triin Lauri, 2017. "Efficiency and fair access in Kindergarten allocation policy design," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 2(1), pages 57-104, December.
    20. Fırat, M. & Briskorn, D. & Laugier, A., 2016. "A Branch-and-Price algorithm for stable workforce assignments with hierarchical skills," European Journal of Operational Research, Elsevier, vol. 251(2), pages 676-685.
    21. Tamás Fleiner, 2003. "A Fixed-Point Approach to Stable Matchings and Some Applications," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 103-126, February.
    22. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    23. H. W. Kuhn, 1955. "The Hungarian method for the assignment problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 2(1‐2), pages 83-97, March.
    24. Daniela Saban & Jay Sethuraman, 2015. "The Complexity of Computing the Random Priority Allocation Matrix," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 1005-1014, October.
    25. Andersson, Tommy, 2017. "Refugee Matching as a Market Design Application," Working Papers 2017:16, Lund University, Department of Economics.
    26. 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.
    27. Peng Shi, 2015. "Guiding School-Choice Reform through Novel Applications of Operations Research," Interfaces, INFORMS, vol. 45(2), pages 117-132, April.
    28. Diebold, Franz & Bichler, Martin, 2017. "Matching with indifferences: A comparison of algorithms in the context of course allocation," European Journal of Operational Research, Elsevier, vol. 260(1), pages 268-282.
    29. Cristina C B Cavalcante & Célio Maschio & Antonio Alberto Santos & Denis Schiozer & Anderson Rocha, 2017. "History matching through dynamic decision-making," PLOS ONE, Public Library of Science, vol. 12(6), pages 1-32, June.
    30. Elliott Peranson & Alvin E. Roth, 1999. "The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design," American Economic Review, American Economic Association, vol. 89(4), pages 748-780, September.
    31. Nitsan Perach & Julia Polak & Uriel Rothblum, 2008. "A stable matching model with an entrance criterion applied to the assignment of students to dormitories at the technion," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 519-535, March.
    Full references (including those not matched with items on IDEAS)

    More about this item


    Assignment; Pareto-efficiency; Welfare-maximization; Complexity; Integerprogrammin;

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    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:has:discpr:2016. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Nora Horvath). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.