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Ties matter: improving efficiency in course allocation by introducing ties

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  • Chen, Ning
  • Li, Mengling

Abstract

We study the course allocation system at Nanyang Technological University, where students submit strict preferences for courses and courses have implicit preferences for students. This formulates a many-to-many matching problem. We show the inefficiencies of the current mechanism and propose new competing mechanisms called Pareto-improving draft and dictatorship mechanisms, which introduce ties into students' preferences. Our mechanisms generate (group) stable and Pareto-efficient allocations, and the dictatorship mechanism can be implemented truthfully. Simulations on real data show that introducing ties into students' preferences can significantly improve efficiency, and the draft mechanism outperforms the dictatorship mechanism despite that the former is non-strategyproof.

Suggested Citation

  • Chen, Ning & Li, Mengling, 2013. "Ties matter: improving efficiency in course allocation by introducing ties," MPRA Paper 47031, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:47031
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    File URL: https://mpra.ub.uni-muenchen.de/47031/1/MPRA_paper_47031.pdf
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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," ULB Institutional Repository 2013/99376, ULB -- Universite Libre de Bruxelles.
    2. Marilda Sotomayor, 2011. "The pareto-stability concept is a natural solution concept for discrete matching markets with indifferences," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(3), pages 631-644, August.
    3. Charles Blair, 1988. "The Lattice Structure of the Set of Stable Matchings with Multiple Partners," Mathematics of Operations Research, INFORMS, vol. 13(4), pages 619-628, November.
    4. Ahmet Alkan, 2002. "A class of multipartner matching markets with a strong lattice structure," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(4), pages 737-746.
    5. Tayfun Sönmez & M. Utku Ünver, 2010. "Course Bidding At Business Schools," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 51(1), pages 99-123, February.
    6. Aytek Erdil & Haluk Ergin, 2008. "What's the Matter with Tie-Breaking? Improving Efficiency in School Choice," American Economic Review, American Economic Association, vol. 98(3), pages 669-689, June.
    7. 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.
    8. Kojima, Fuhito & Manea, Mihai, 2010. "Incentives in the probabilistic serial mechanism," Journal of Economic Theory, Elsevier, vol. 145(1), pages 106-123, January.
    9. Martinez, Ruth & Masso, Jordi & Neme, Alejandro & Oviedo, Jorge, 2004. "An algorithm to compute the full set of many-to-many stable matchings," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 187-210, March.
    10. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
    11. Tayfun Sönmez & M. Utku Ünver, 2009. "Matching, Allocation, and Exchange of Discrete Resources," Boston College Working Papers in Economics 717, Boston College Department of Economics.
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    More about this item

    Keywords

    matching; many-to-many; Pareto efficiency; stability; strategyproof;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • I23 - Health, Education, and Welfare - - Education - - - Higher Education; Research Institutions

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