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Competitive Equilibrium from Equal Incomes for Two-Sided Matching

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  • He, Yinghua
  • Yan, Jianye

Abstract

Competitive Equilibrium from Equal Incomes for Two-Sided Matching Using the assignment of students to schools as our leading example, we study many-to-one two-sided matching markets without transfers. Students are endowed with cardinal preferences and schools with ordinal ones, while preferences of both sides need not be strict. Using the idea of a competitive equilibrium from equal incomes (CEEI, Hylland and Zeckhauser (1979)), we propose a new mechanism, the Generalized CEEI, in which students face different prices depending on how schools rank them. It always produces fair (justified-envy-free) and ex ante e¢ cient random assignments and stable deterministic assignments if both students and schools are truth-telling. We show that each student's incentive to misreport vanishes when the market becomes large, given all others are truthful. The mechanism is particularly relevant to school choice as schools' priority orderings over students are usually known and can be considered as their ordinal preferences. More importantly, in settings like school choice where agents have similar ordinal preferences, the mechanismis explicit use of cardinal preferences may significantly improve eficiency. We also discuss its application in school choice with group-specific quotas and in one-sided matching.

Suggested Citation

  • He, Yinghua & Yan, Jianye, 2012. "Competitive Equilibrium from Equal Incomes for Two-Sided Matching," TSE Working Papers 12-344, Toulouse School of Economics (TSE).
  • Handle: RePEc:tse:wpaper:26415
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    References listed on IDEAS

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    1. Atila Abdulkadiro?lu & Yeon-Koo Che & Yosuke Yasuda, 2015. "Expanding "Choice" in School Choice," American Economic Journal: Microeconomics, American Economic Association, vol. 7(1), pages 1-42, February.
    2. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-proofness versus Efficiency in Matching with Indifferences: Redesigning the New York City High School Match," NBER Working Papers 14864, National Bureau of Economic Research, Inc.
    3. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
    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. He, Yinghua, 2012. "Gaming the Boston School Choice Mechanism in Beijing," TSE Working Papers 12-345, Toulouse School of Economics (TSE).
    6. Fuhito Kojima & Parag A. Pathak, 2009. "Incentives and Stability in Large Two-Sided Matching Markets," American Economic Review, American Economic Association, vol. 99(3), pages 608-627, June.
    7. Charles M. Tiebout, 1956. "A Pure Theory of Local Expenditures," Journal of Political Economy, University of Chicago Press, vol. 64, pages 416-416.
    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. Yeon-Koo Che & Fuhito Kojima, 2010. "Asymptotic Equivalence of Probabilistic Serial and Random Priority Mechanisms," Econometrica, Econometric Society, vol. 78(5), pages 1625-1672, September.
    10. Roberts, Donald John & Postlewaite, Andrew, 1976. "The Incentives for Price-Taking Behavior in Large Exchange Economies," Econometrica, Econometric Society, vol. 44(1), pages 115-127, January.
    11. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-Proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match," American Economic Review, American Economic Association, vol. 99(5), pages 1954-1978, December.
    12. Kesten, Onur, 2006. "On two competing mechanisms for priority-based allocation problems," Journal of Economic Theory, Elsevier, vol. 127(1), pages 155-171, March.
    13. Sonmez, Tayfun, 1997. "Manipulation via Capacities in Two-Sided Matching Markets," Journal of Economic Theory, Elsevier, vol. 77(1), pages 197-204, November.
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    Cited by:

    1. Antonio Miralles, 2015. "Sequential Pseudomarkets: Welfare Economics in Random Assignment Economies," Working Papers 699, Barcelona Graduate School of Economics.
    2. He, Yinghua & Li, Sanxi & Yan, Jianye, 2015. "Evaluating assignment without transfers: A market perspective," Economics Letters, Elsevier, vol. 133(C), pages 40-44.
    3. He, Yinghua, 2012. "Gaming the Boston School Choice Mechanism in Beijing," TSE Working Papers 12-345, Toulouse School of Economics (TSE).
    4. Kesten, Onur & Kurino, Morimitsu & Nesterov, Alexander, 2015. "Efficient lottery design," Discussion Papers, Research Unit: Market Behavior SP II 2015-203, Social Science Research Center Berlin (WZB).
    5. He, Yinghua & Miralles, Antonio & Pycia, Marek & Yan, Jianye, 2015. "A Pseudo-Market Approach to Allocation with Priorities," TSE Working Papers 15-601, Toulouse School of Economics (TSE), revised Jul 2017.

    More about this item

    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
    • I29 - Health, Education, and Welfare - - Education - - - Other

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