School choice: Nash implementation of stable matchings through rank-priority mechanisms

Paula Jaramillo, Cagatay Kayi and Flip Klijn

Journal of Mathematical Economics, 2021, vol. 95, issue C

Abstract: We consider school choice problems (Abdulkadiroğlu and Sönmez, 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 matchings (Theorem 1). Our second main result is a strong impossibility result: under incomplete information, no rank-priority mechanism implements the set of stable matchings (Theorem 2).

Keywords: School choice; Rank-priority mechanisms; Stability; Nash implementation (search for similar items in EconPapers)
Date: 2021
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Related works:
Working Paper: School Choice: Nash Implementation of Stable Matchings through Rank-Priority Mechanisms (2017)
Working Paper: School Choice: Nash Implementation of Stable Matchings through Rank-Priority Mechanisms (2017)
Working Paper: School Choice: Nash Implementation of Stable Matchings through Rank-Priority Mechanisms (2017)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:95:y:2021:i:c:s0304406821000343

DOI: 10.1016/j.jmateco.2021.102496

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