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Stability and strategy-proofness for college admissions with an eligibility criterion

Author

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  • Azar Abizada
  • Siwei Chen

Abstract

We study college admissions with an eligibility criterion. Each college has strict preferences over the sets of students and each student has strict preferences over the colleges. Each student receives a score from a central exam. The students are endogenously divided into two groups: those who are eligible to apply to colleges, and those who are not. Eligibility respects the students’ scores. We extend the college admissions model with eligibility criterion studied by Perach and Rothblum in Int (J Game Theory 39:657–667 ( 2010 )) to a general case where different students may obtain the same scores from the central exam. We introduce three notions of stability that respect eligibility. We define three new rules based on the McVitie-Wilson algorithm, each of which satisfies different notions of stability. We also study incentive compatibility. We show that two of our rules are immune to strategic manipulations. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Azar Abizada & Siwei Chen, 2015. "Stability and strategy-proofness for college admissions with an eligibility criterion," Review of Economic Design, Springer;Society for Economic Design, vol. 19(1), pages 47-66, March.
    • Handle: RePEc:spr:reecde:v:19:y:2015:i:1:p:47-66
    DOI: 10.1007/s10058-014-0163-4
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    References listed on IDEAS

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    1. Alvin Roth, 2008. "Deferred acceptance algorithms: history, theory, practice, and open questions," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 537-569, March.
    2. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth & Tayfun Sönmez, 2005. "The Boston Public School Match," American Economic Review, American Economic Association, vol. 95(2), pages 368-371, May.
    3. 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.
    4. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August.
    5. 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.
    6. 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.
    7. Nitsan Perach & Uriel Rothblum, 2010. "Incentive compatibility for the stable matching model with an entrance criterion," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 657-667, October.
    8. Chen, Yan & Onur, Kesten, 2013. "From Boston to Chinese parallel to deferred acceptance: Theory and experiments on a family of school choice mechanisms," Discussion Papers, Research Unit: Market Behavior SP II 2013-205, WZB Berlin Social Science Center.
    9. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    10. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-1480, November.
    11. Balinski, Michel & Sonmez, Tayfun, 1999. "A Tale of Two Mechanisms: Student Placement," Journal of Economic Theory, Elsevier, vol. 84(1), pages 73-94, January.
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    2. Hafalir, Isa E. & Hakimov, Rustamdjan & Kübler, Dorothea & Kurino, Morimitsu, 2018. "College admissions with entrance exams: Centralized versus decentralized," Journal of Economic Theory, Elsevier, vol. 176(C), pages 886-934.
    3. Stylianos Despotakis & Isa Hafalir & R. Ravi & Amin Sayedi, 2017. "Expertise in Online Markets," Management Science, INFORMS, vol. 63(11), pages 3895-3910, November.

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    More about this item

    Keywords

    College admissions; Eligibility; Quasi-stability ; Justifiable-stability; Strategy-proofness; C78; D63;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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