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This notion is used to axiomatically characterize the core on the domain of convex games. Moreover, we characterize all nonempty solutions satisfying individual rationality, anonymity, scale covariance, superadditivity, weak Hart\u2013Mas-Colell consistency, and converse Hart\u2013Mas-Colell consistency. This family consists of (a) the Shapley value, (b) all homothetic images of the core with the Shapley value as center of homothety and with positive ratios of homothety not larger than one, and (c) their relative interiors.<\/jats:p>","DOI":"10.1007\/s00182-021-00798-6","type":"journal-article","created":{"date-parts":[[2021,10,8]],"date-time":"2021-10-08T02:24:38Z","timestamp":1633659878000},"page":"413-429","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Hart\u2013Mas-Colell consistency and the core in convex games"],"prefix":"10.1007","volume":"51","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8023-0273","authenticated-orcid":false,"given":"Bas","family":"Dietzenbacher","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter","family":"Sudh\u00f6lter","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,10,6]]},"reference":[{"issue":"2","key":"798_CR1","doi-asserted-by":"publisher","first-page":"260","DOI":"10.1016\/j.geb.2006.08.002","volume":"59","author":"C Chang","year":"2007","unstructured":"Chang C, Hu C (2007) Reduced game and converse consistency. 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