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School Choice: Nash Implementation of Stable Matchings through Rank-Priority Mechanisms

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  • Paula Jaramillo
  • Ça?atay Kay?
  • Flip Klijn

Abstract

We consider school choice problems (Abdulkadiroğlu and Sonmez, 2003) where students are assigned to public schools through a centralized assignment mechanism. We study the family of so-called rank-priority mechanisms, each of which is induced by an order of rank-priority pairs. Following the corresponding order of pairs, at each step a rank-priority mechanism considers a rank-priority pair and matches an available student to an unfilled school if the student and the school rank and prioritize each other in accordance with the rank-priority pair. The Boston or immediate acceptance mechanism is a particular rank-priority mechanism. Our first main result is a characterization of the subfamily of rank-priority mechanisms that Nash implement the set of stable (i.e., fair) matchings (Theorem 1). We show that our characterization also holds for “sub-implementation†and “sup-implementation†(Corollaries 3 and 4). Our second main result is a strong impossibility result: under incomplete information, no rank-priority mechanism implements the set of stable matchings (Theorem 2).

Suggested Citation

  • Paula Jaramillo & Ça?atay Kay? & Flip Klijn, 2017. "School Choice: Nash Implementation of Stable Matchings through Rank-Priority Mechanisms," Documentos de Trabajo 015501, Universidad del Rosario.
  • Handle: RePEc:col:000092:015501
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    References listed on IDEAS

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    More about this item

    Keywords

    School choice; rank-priority mechanisms; stability; Nash implementation;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • I20 - Health, Education, and Welfare - - Education - - - General

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