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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

    as
    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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