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Course Match: A Large-Scale Implementation of Approximate Competitive Equilibrium from Equal Incomes for Combinatorial Allocation

Author

Listed:
  • Eric Budish

    (University of Chicago, Chicago, Illinois 60637)

  • Gérard P. Cachon

    (University of Pennsylvania, Philadelphia, Pennsylvania 19104)

  • Judd B. Kessler

    (University of Pennsylvania, Philadelphia, Pennsylvania 19104)

  • Abraham Othman

    (University of Pennsylvania, Philadelphia, Pennsylvania 19104)

Abstract

Combinatorial allocation involves assigning bundles of items to agents when the use of money is not allowed. Course allocation is one common application of combinatorial allocation, in which the bundles are schedules of courses and the assignees are students. Existing mechanisms used in practice have been shown to have serious flaws, which lead to allocations that are inefficient, unfair, or both. A recently developed mechanism is attractive in theory but has several features that limit its feasibility for practice. This paper reports on the design and implementation of a new course allocation mechanism, Course Match, that is suitable in practice. To find allocations, Course Match performs a massive parallel heuristic search that solves billions of mixed-integer programs to output an approximate competitive equilibrium in a fake-money economy for courses. Quantitative summary statistics for two semesters of full-scale use at a large business school (the Wharton School of Business, which has about 1,700 students and up to 350 courses in each semester) demonstrate that Course Match is both fair and efficient, a finding reinforced by student surveys showing large gains in satisfaction and perceived fairness.

Suggested Citation

  • Eric Budish & Gérard P. Cachon & Judd B. Kessler & Abraham Othman, 2017. "Course Match: A Large-Scale Implementation of Approximate Competitive Equilibrium from Equal Incomes for Combinatorial Allocation," Operations Research, INFORMS, vol. 65(2), pages 314-336, April.
    • Handle: RePEc:inm:oropre:v:65:y:2017:i:2:p:314-336
    DOI: 10.1287/opre.2016.1544
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    References listed on IDEAS

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    1. Eric Budish & Estelle Cantillon, 2012. "The Multi-unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard," American Economic Review, American Economic Association, vol. 102(5), pages 2237-2271, August.
    2. Aradhna Krishna & M. Utku Ünver, 2008. "Research Note—Improving the Efficiency of Course Bidding at Business Schools: Field and Laboratory Studies," Marketing Science, INFORMS, vol. 27(2), pages 262-282, 03-04.
    3. Alvin E. Roth, 2002. "The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics," Econometrica, Econometric Society, vol. 70(4), pages 1341-1378, July.
    4. 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.
    5. 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.
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    Cited by:

    1. Alexander Teytelboym & Shengwu Li & Scott Duke Kominers & Mohammad Akbarpour & Piotr Dworczak, 2021. "Discovering Auctions: Contributions of Paul Milgrom and Robert Wilson," Scandinavian Journal of Economics, Wiley Blackwell, vol. 123(3), pages 709-750, July.
    2. Kyle Greenberg & Parag A. Pathak & Tayfun Sönmez, 2020. "Mechanism Design meets Priority Design: Redesigning the US Army’s Branching Process Through Market Design," Boston College Working Papers in Economics 1035, Boston College Department of Economics.
    3. Battal Dou{g}an & Kenzo Imamura & M. Bumin Yenmez, 2022. "Market Design with Deferred Acceptance: A Recipe for Policymaking," Papers 2209.06777, arXiv.org.
    4. Nikhil Agarwal & Eric Budish, 2021. "Market Design," NBER Working Papers 29367, National Bureau of Economic Research, Inc.
    5. P'eter Bir'o & M'arton Gyetvai, 2021. "Online voluntary mentoring: Optimising the assignment of students and mentors," Papers 2102.06671, arXiv.org.
    6. Julien Combe & Vladyslav Nora & Olivier Tercieux, 2021. "Dynamic assignment without money: Optimality of spot mechanisms," Working Papers 2021-11, Center for Research in Economics and Statistics.
    7. Andrea Canidio, 2023. "Auctions with Tokens: Monetary Policy as a Mechanism Design Choice," Papers 2301.13794, arXiv.org, revised Aug 2023.
    8. Eric Budish & Judd B. Kessler, 2022. "Can Market Participants Report Their Preferences Accurately (Enough)?," Management Science, INFORMS, vol. 68(2), pages 1107-1130, February.
    9. Biró, Péter & Klijn, Flip & Pápai, Szilvia, 2022. "Serial Rules in a Multi-Unit Shapley-Scarf Market," Games and Economic Behavior, Elsevier, vol. 136(C), pages 428-453.
    10. Federico Echenique & Sumit Goel & SangMok Lee, 2022. "Stable allocations in discrete exchange economies," Papers 2202.04706, arXiv.org, revised Feb 2024.
    11. Matteo Aquilina & Eric Budish & Peter O'Neill, 2021. "Quantifying the high-frequency trading "arms race"," BIS Working Papers 955, Bank for International Settlements.
    12. Kyle Greenberg & Parag A. Pathak & Tayfun Sonmez, 2021. "Mechanism Design meets Priority Design: Redesigning the US Army's Branching Process," Papers 2106.06582, arXiv.org.
    13. Eric Budish & Robin S. Lee & John J. Shim, 2019. "A Theory of Stock Exchange Competition and Innovation: Will the Market Fix the Market?," NBER Working Papers 25855, National Bureau of Economic Research, Inc.
    14. Eric Budish & Peter Cramton & Albert S. Kyle & Jeongmin Lee & David Malec, 2022. "Flow Trading," ECONtribute Discussion Papers Series 146, University of Bonn and University of Cologne, Germany.
    15. Martin Bichler & Soeren Merting, 2021. "Randomized Scheduling Mechanisms: Assigning Course Seats in a Fair and Efficient Way," Production and Operations Management, Production and Operations Management Society, vol. 30(10), pages 3540-3559, October.
    16. Yan Chen & Peter Cramton & John A. List & Axel Ockenfels, 2021. "Market Design, Human Behavior, and Management," Management Science, INFORMS, vol. 67(9), pages 5317-5348, September.
    17. Shivam Gupta & Wei Chen & Milind Dawande & Ganesh Janakiraman, 2023. "Three Years, Two Papers, One Course Off: Optimal Nonmonetary Reward Policies," Management Science, INFORMS, vol. 69(5), pages 2852-2869, May.
    18. Biró, Péter & Gyetvai, Márton, 2023. "Online voluntary mentoring: Optimising the assignment of students and mentors," European Journal of Operational Research, Elsevier, vol. 307(1), pages 392-405.
    19. Laschever, Ron A. & Weinstein, Russell, 2021. "Preference Signaling and Worker-Firm Matching: Evidence from Interview Auctions," IZA Discussion Papers 14622, Institute of Labor Economics (IZA).
    20. Thomas L. Magnanti & Karthik Natarajan, 2018. "Allocating Students to Multidisciplinary Capstone Projects Using Discrete Optimization," Interfaces, INFORMS, vol. 48(3), pages 204-216, June.
    21. Budish, Eric & Reny, Philip J., 2020. "An improved bound for the Shapley–Folkman theorem," Journal of Mathematical Economics, Elsevier, vol. 89(C), pages 48-52.

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