Constrained-optimal tradewise-stable outcomes in the one-sided assignment game

In the one-sided assignment game, any two agents can form a trade; they can decide to form a partnership and agree on how to share the surplus created. Contrary to the two-sided assignment game, stable outcomes often fail to exist in the one-sided assignment game. Hence the core, which coincides wit...

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Detalles Bibliográficos
Autores: Pérez Castrillo, David|||0000-0002-1840-7621, Sotomayor, Marilda
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:270390
Acceso en línea:https://ddd.uab.cat/record/270390
https://dx.doi.org/urn:doi:10.1007/s00199-022-01483-9
Access Level:acceso abierto
Palabra clave:Matching
Assignment game
Stability
Core
Trade
Tradewise-stable
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spelling Constrained-optimal tradewise-stable outcomes in the one-sided assignment gamea solution concept weaker than the corePérez Castrillo, David|||0000-0002-1840-7621Sotomayor, MarildaMatchingAssignment gameStabilityCoreTradeTradewise-stableIn the one-sided assignment game, any two agents can form a trade; they can decide to form a partnership and agree on how to share the surplus created. Contrary to the two-sided assignment game, stable outcomes often fail to exist in the one-sided assignment game. Hence the core, which coincides with the set of stable payoffs, may be empty. We introduce the idea of tradewise-stable (t-stable) outcomes: they are individually rational outcomes where all trades are stable; that is, no matched agent can form a blocking pair with any other agent, neither matched nor unmatched. We propose the set of constrained-optimal (optimal) t-stable outcomes, the set of the maximal elements of the set of t-stable outcomes, as a natural solution concept for this game. We prove that this set is non-empty, it coincides with the set of stable outcomes when the core is non-empty, and it satisfies similar properties to the set of stable outcomes even when the core is empty. We propose a partnership formation process that starts withthe outcome where every player stands alone, goes through steps where the set of active players expands, always forming t-stable outcomes, and ends in an (in any) optimal t-stable outcome. Finally, we also use the new concept to establish conditions under which the core is non-empty. 22023-01-0120232023-01-01Articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/270390https://dx.doi.org/urn:doi:10.1007/s00199-022-01483-9reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengAgencia Estatal de Investigación https://doi.org/10.13039/501100011033 PGC2018-094348-B-I00Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-711Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 CEX2019-000915-Sopen accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2703902026-06-06T12:50:31Z
dc.title.none.fl_str_mv Constrained-optimal tradewise-stable outcomes in the one-sided assignment game
a solution concept weaker than the core
title Constrained-optimal tradewise-stable outcomes in the one-sided assignment game
spellingShingle Constrained-optimal tradewise-stable outcomes in the one-sided assignment game
Pérez Castrillo, David|||0000-0002-1840-7621
Matching
Assignment game
Stability
Core
Trade
Tradewise-stable
title_short Constrained-optimal tradewise-stable outcomes in the one-sided assignment game
title_full Constrained-optimal tradewise-stable outcomes in the one-sided assignment game
title_fullStr Constrained-optimal tradewise-stable outcomes in the one-sided assignment game
title_full_unstemmed Constrained-optimal tradewise-stable outcomes in the one-sided assignment game
title_sort Constrained-optimal tradewise-stable outcomes in the one-sided assignment game
dc.creator.none.fl_str_mv Pérez Castrillo, David|||0000-0002-1840-7621
Sotomayor, Marilda
author Pérez Castrillo, David|||0000-0002-1840-7621
author_facet Pérez Castrillo, David|||0000-0002-1840-7621
Sotomayor, Marilda
author_role author
author2 Sotomayor, Marilda
author2_role author
dc.subject.none.fl_str_mv Matching
Assignment game
Stability
Core
Trade
Tradewise-stable
topic Matching
Assignment game
Stability
Core
Trade
Tradewise-stable
description In the one-sided assignment game, any two agents can form a trade; they can decide to form a partnership and agree on how to share the surplus created. Contrary to the two-sided assignment game, stable outcomes often fail to exist in the one-sided assignment game. Hence the core, which coincides with the set of stable payoffs, may be empty. We introduce the idea of tradewise-stable (t-stable) outcomes: they are individually rational outcomes where all trades are stable; that is, no matched agent can form a blocking pair with any other agent, neither matched nor unmatched. We propose the set of constrained-optimal (optimal) t-stable outcomes, the set of the maximal elements of the set of t-stable outcomes, as a natural solution concept for this game. We prove that this set is non-empty, it coincides with the set of stable outcomes when the core is non-empty, and it satisfies similar properties to the set of stable outcomes even when the core is empty. We propose a partnership formation process that starts withthe outcome where every player stands alone, goes through steps where the set of active players expands, always forming t-stable outcomes, and ends in an (in any) optimal t-stable outcome. Finally, we also use the new concept to establish conditions under which the core is non-empty.
publishDate 2023
dc.date.none.fl_str_mv 2
2023-01-01
2023
2023-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/270390
https://dx.doi.org/urn:doi:10.1007/s00199-022-01483-9
url https://ddd.uab.cat/record/270390
https://dx.doi.org/urn:doi:10.1007/s00199-022-01483-9
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 PGC2018-094348-B-I00
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-711
Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 CEX2019-000915-S
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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