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

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 corresp...

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Autores Principales: Jaramillo, Paula, Kayi, Cagatay, Klijn, Flip
Formato: Documento de trabajo (Working Paper)
Lenguaje:Español (Spanish)
Publicado: Universidad del Rosario 2017
Materias:
C78
D61
D78
I20
Acceso en línea:http://repository.urosario.edu.co//handle/10336/13235
id ir-10336-13235
recordtype dspace
spelling ir-10336-132352019-09-19T12:37:01Z School Choice: Nash Implementation of Stable Matchings through Rank-Priority Mechanisms Jaramillo, Paula Kayi, Cagatay Klijn, Flip Probabilidades & matemáticas aplicadas Teoría de los juegos Equilibrio (Economía) Nash implementation School choice Rank-priority mechanisms Stability C78 D61 D78 I20 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 (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). 2017 2017-04-04T16:33:14Z info:eu-repo/semantics/workingPaper info:eu-repo/semantics/publishedVersion http://repository.urosario.edu.co//handle/10336/13235 spa info:eu-repo/semantics/openAccess application/pdf Universidad del Rosario Facultad de Economía reponame:Repositorio Institucional EdocUR instname:Universidad del Rosario
institution EdocUR - Universidad del Rosario
collection DSpace
language Español (Spanish)
topic Probabilidades & matemáticas aplicadas
Teoría de los juegos
Equilibrio (Economía)
Nash implementation
School choice
Rank-priority mechanisms
Stability
C78
D61
D78
I20
spellingShingle Probabilidades & matemáticas aplicadas
Teoría de los juegos
Equilibrio (Economía)
Nash implementation
School choice
Rank-priority mechanisms
Stability
C78
D61
D78
I20
Jaramillo, Paula
Kayi, Cagatay
Klijn, Flip
School Choice: Nash Implementation of Stable Matchings through Rank-Priority Mechanisms
description 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 (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).
format Documento de trabajo (Working Paper)
author Jaramillo, Paula
Kayi, Cagatay
Klijn, Flip
author_facet Jaramillo, Paula
Kayi, Cagatay
Klijn, Flip
author_sort Jaramillo, Paula
title School Choice: Nash Implementation of Stable Matchings through Rank-Priority Mechanisms
title_short School Choice: Nash Implementation of Stable Matchings through Rank-Priority Mechanisms
title_full School Choice: Nash Implementation of Stable Matchings through Rank-Priority Mechanisms
title_fullStr School Choice: Nash Implementation of Stable Matchings through Rank-Priority Mechanisms
title_full_unstemmed School Choice: Nash Implementation of Stable Matchings through Rank-Priority Mechanisms
title_sort school choice: nash implementation of stable matchings through rank-priority mechanisms
publisher Universidad del Rosario
publishDate 2017
url http://repository.urosario.edu.co//handle/10336/13235
_version_ 1645141208128815104
score 11,369763