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Competitive Equilibrium from Equal Incomes for Two-Sided Matching

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  • Yinghua He
  • Antonio Miralles
  • Jianye Yan

Abstract

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 efficient random assignments and stable deterministic ones with respect to stated preferences. Moreover, if a group of students are top ranked by all schools, the G-CEEI random assignment is ex ante weakly efficient with respect to students’ welfare. 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 since schools’ priority orderings can be considered as their ordinal preferences. More importantly, in settings where agents have similar ordinal preferences, the mechanism’s explicit use of cardinal preferences may significantly improve efficiency. We also discuss its application in school choice with affirmative action such as group-specific quotas and in one-sided matching.

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Bibliographic Info

Paper provided by Barcelona Graduate School of Economics in its series Working Papers with number 692.

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Date of creation: Dec 2012
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Handle: RePEc:bge:wpaper:692

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Keywords: two-sided matching; weak preferences; school choice; efficiency; fairness; stability; incentive compatibility; competitive equilibrium from equal incomes;

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References

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  1. Sonmez, Tayfun, 1997. "Manipulation via Capacities in Two-Sided Matching Markets," Journal of Economic Theory, Elsevier, vol. 77(1), pages 197-204, November.
  2. Atila Abdulkadiroglu & Yeon-Koo Che & Yosuke Yasuda, 2010. "Expanding 'Choice' in School Choice," Working Papers 10-23, Duke University, Department of Economics.
  3. Charles M. Tiebout, 1956. "A Pure Theory of Local Expenditures," Journal of Political Economy, University of Chicago Press, vol. 64, pages 416.
  4. Roberts, Donald John & Postlewaite, Andrew, 1976. "The Incentives for Price-Taking Behavior in Large Exchange Economies," Econometrica, Econometric Society, vol. 44(1), pages 115-27, January.
  5. He, Yinghua, 2012. "Gaming the Boston School Choice Mechanism in Beijing," TSE Working Papers 12-345, Toulouse School of Economics (TSE).
  6. 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.
  7. Kesten, Onur, 2006. "On two competing mechanisms for priority-based allocation problems," Journal of Economic Theory, Elsevier, vol. 127(1), pages 155-171, March.
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Cited by:
  1. Antonio Miralles, 2013. "Sequential Pseudomarkets: Welfare Economics in Random Assignment Economies," Working Papers 699, Barcelona Graduate School of Economics.

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