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Stable Matching Games

hal.structure.identifierLaboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
dc.contributor.authorGarrido Lucero, Felipe
hal.structure.identifierLaboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
dc.contributor.authorLaraki, Rida
HAL ID: 179670
ORCID: 0000-0002-4898-2424
dc.date.accessioned2022-02-16T11:38:39Z
dc.date.available2022-02-16T11:38:39Z
dc.date.issued2021
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22654
dc.language.isoenen
dc.subjectStable Matchingen
dc.subjectGeneralized Nash Equilibriumen
dc.subjectZero-sum Gamesen
dc.subjectPotential Gamesen
dc.subjectInfinitely repeated Gamesen
dc.subjectMatching with Contracten
dc.subjectMatching with Transferen
dc.subject.ddc004en
dc.titleStable Matching Gamesen
dc.typeDocument de travail / Working paper
dc.description.abstractenGale and Shapley introduced a matching problem between two sets of agents where each agent on one side has an exogenous preference ordering over the agents on the other side. They defined a matching as stable if no unmatched pair can both improve their utility by forming a new pair. They proved, algorithmically, the existence of a stable matching. Shapley and Shubik, Demange and Gale, and many others extended the model by allowing monetary transfers. We offer a further extension by assuming that matched couples obtain their payoff endogenously as the outcome of a strategic game they have to play in a usual non-cooperative sense (without commitment) or in a semi-cooperative way (with commitment, as the outcome of a bilateral binding contract in which each player is responsible for his/her part of the contract). Depending on whether the players can commit or not, we define in each case a solution concept that combines Gale-Shapley pairwise stability with a (generalized) Nash equilibrium stability. In each case, we give the necessary and sufficient conditions for the set of stable allocations to be non-empty, we study its geometry (full/semi-lattice), and provide an algorithm that converges to its maximal element. Finally, we prove that our second model (with commitment) encompasses and refines most of the literature (matching with monetary transfers as well as matching with contracts).en
dc.publisher.cityParisen
dc.relation.ispartofseriestitlePreprint Lamsadeen
dc.subject.ddclabelInformatique généraleen
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dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2022-02-16T11:36:50Z
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