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dc.contributor.authorCrettez, Bertrand
dc.contributor.authorHayek, Naila
dc.contributor.authorMartín Herrán, Guiomar 
dc.date.accessioned2024-10-11T07:46:48Z
dc.date.available2024-10-11T07:46:48Z
dc.date.issued2024
dc.identifier.citationEuropean Journal of Operational Researches
dc.identifier.issn0377-2217es
dc.identifier.urihttps://uvadoc.uva.es/handle/10324/70754
dc.description.abstractWe study supply chain competition and vertical coordination in a linear-quadratic differential game setting. In this setting, supply chains produce complementary goods and each of them includes a single manufacturer and a single retailer who coordinate their decisions through a revenue-sharing contract including a wholesale price and a fixed sales revenue share. We study a multiple leader-follower Stackelberg game where the manufacturers are the leaders and the retailers are the followers. Competition occurs at both levels of the supply chains. Retailers play Nash and compete in price; manufacturers also play Nash but they compete in choosing their production capacities by exploiting the equilibrium price decisions made by the retailers. We show that open-loop Nash equilibria exist when the manufacturers only receive a wholesale price (there are no longer exploiting the equilibrium price decision made by the retailers, however). When the manufacturers receive both a wholesale-price and a share of the retailers' sales revenues, equilibria generally no longer exist. The non-existence of an equilibrium stems from the fact that the manufacturers' instant profits are discontinuous functions of their production capacities. This discontinuity leads to a major technical difficulty in that one cannot apply standard optimal control approaches to study the equilibria of the dynamic game. Our results illustrate the possibility that competition between supply chains might not be sustainable when they sell complementary products and rely on a revenue-sharing agreement.es
dc.format.mimetypeapplication/pdfes
dc.language.isospaes
dc.rights.accessRightsinfo:eu-repo/semantics/openAccesses
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.titleExistence of equilibrium in a dynamic supply chain game with vertical coordination, horizontal competition, and complementary goodses
dc.typeinfo:eu-repo/semantics/articlees
dc.identifier.doi10.1016/j.ejor.2024.09.027es
dc.identifier.publicationtitleEuropean Journal of Operational Researches
dc.peerreviewedSIes
dc.description.projectEste trabajo ha sido parcialmente financiado por la AEI (Agencia Estatal de Investigación) a través de los proyectos PID2020-112509GB-I00 y TED2021-130390B-I00es
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional*
dc.type.hasVersioninfo:eu-repo/semantics/draftes


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