{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:44:16Z","timestamp":1740109456226,"version":"3.37.3"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2021,6,2]],"date-time":"2021-06-02T00:00:00Z","timestamp":1622592000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,6,2]],"date-time":"2021-06-02T00:00:00Z","timestamp":1622592000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100007195","name":"Universit\u00e0 degli Studi di Napoli Federico II","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100007195","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int J Game Theory"],"published-print":{"date-parts":[[2021,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, we study the problem of a fair redistribution of resources among agents in an exchange economy \u00e1 la Shitovitz (Econometrica 41:467\u2013501, 1973), with agents\u2019 measure space having both atoms and an atomless sector. We proceed by following the idea of Aubin (Mathematical methods of game economic theory. North-Holland, Amsterdam, New York, Oxford, 1979) to allow for partial participation of individuals in coalitions, that induces an enlargement of the set of ordinary coalitions to the so-called fuzzy or generalized coalitions. We propose a notion of fairness which, besides efficiency, imposes absence of envy towards fuzzy coalitions, and which fully characterizes competitive equilibria and Aubin-core allocations.<\/jats:p>","DOI":"10.1007\/s00182-021-00780-2","type":"journal-article","created":{"date-parts":[[2021,6,2]],"date-time":"2021-06-02T07:03:54Z","timestamp":1622617434000},"page":"1033-1052","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Fairness and fuzzy coalitions"],"prefix":"10.1007","volume":"50","author":[{"given":"Chiara","family":"Donnini","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3663-6468","authenticated-orcid":false,"given":"Marialaura","family":"Pesce","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,6,2]]},"reference":[{"key":"780_CR1","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/s00182-007-0105-2","volume":"37","author":"N Allouch","year":"2008","unstructured":"Allouch N, Predtetchinski A (2008) On the non-emptiness of the fuzzy core. Int J Game Theory 37:203\u2013210","journal-title":"Int J Game Theory"},{"key":"780_CR2","unstructured":"Aubin J (ed) (1979) Mathematical methods of game economic theory. North-Holland, Amsterdam, New York, Oxford"},{"key":"780_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00182-007-0093-2","volume":"36","author":"Y Azrieli","year":"2007","unstructured":"Azrieli Y, Lehrer E (2007) On some families of cooperative fuzzy games. Int J Game Theory 36:1\u201315","journal-title":"Int J Game Theory"},{"key":"780_CR4","doi-asserted-by":"publisher","first-page":"573","DOI":"10.1007\/s11238-013-9386-z","volume":"76","author":"A Basile","year":"2014","unstructured":"Basile A, Graziano MG, Pesce M (2014) On fairness of equilibria in economies with differential information. Theory Decis 76:573\u2013599","journal-title":"Theory Decis"},{"key":"780_CR5","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1007\/s00712-017-0543-7","volume":"123","author":"A Basile","year":"2018","unstructured":"Basile A, Graziano MG, Tarantino C (2018) Coalitional fairness with participation rates. J Econ 123:97\u2013139","journal-title":"J Econ"},{"key":"780_CR6","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1016\/j.jmateco.2014.11.005","volume":"56","author":"A Bhowmik","year":"2015","unstructured":"Bhowmik A, Graziano MG (2015) On Vind\u2019s theorem for an economy with atoms and infinitely many commodities. J Math Econ 56:26\u201336","journal-title":"J Math Econ"},{"key":"780_CR7","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1016\/j.mathsocsci.2010.01.002","volume":"59","author":"S Cato","year":"2010","unstructured":"Cato S (2010) Local strict envy-freeness in large economies. Math Soc Sci 59:319\u2013322","journal-title":"Math Soc Sci"},{"key":"780_CR8","doi-asserted-by":"crossref","unstructured":"Donnini C, Pesce M (2020) Strict fairness of equilibria in asymmetric information economies and mixed markets. Econ Theory 69:107\u2013124","DOI":"10.1007\/s00199-018-1158-0"},{"key":"780_CR9","doi-asserted-by":"crossref","unstructured":"Donnini C, Pesce M (2021) Absence of envy among \u201cneighbors\u201d can be enough. BE J Theor Econ 21(1):187\u2013204","DOI":"10.1515\/bejte-2020-0019"},{"issue":"6","key":"780_CR10","first-page":"995","volume":"64","author":"A Feldman","year":"1974","unstructured":"Feldman A, Kirman A (1974) Fairness and envy. Am Econ Rev 64(6):995\u20131005","journal-title":"Am Econ Rev"},{"key":"780_CR11","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1016\/0022-247X(90)90262-E","volume":"153","author":"M Florenzano","year":"1990","unstructured":"Florenzano M (1990) Edgeworth equilibria, fuzzy core and equilibria of a production economy without ordered preferences. J Math Anal Appl 153:18\u201336","journal-title":"J Math Anal Appl"},{"key":"780_CR12","unstructured":"Foley D (1967) Resource allocation and the public sector. Yale Econ Essays 7:45\u201398"},{"key":"780_CR13","doi-asserted-by":"crossref","unstructured":"Gabszewicz JJ, Mertens J (1971) An equivalence theorem for the core of an economy whose atoms are not \u201cToo\u201d Big. Econometrica 39:713\u2013721","DOI":"10.2307\/1909574"},{"key":"780_CR14","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1007\/BF01209704","volume":"3","author":"J Garc\u00eda-Cutr\u00edn","year":"1993","unstructured":"Garc\u00eda-Cutr\u00edn J, Herv\u00e9s-Beloso C (1993) A discrete approach to continuum economies. Econ Theory 3:577\u2013583","journal-title":"Econ Theory"},{"key":"780_CR15","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1016\/j.jmateco.2020.08.008","volume":"91","author":"MG Graziano","year":"2020","unstructured":"Graziano MG, Pesce M, Urbinati N (2020) Generalized Coalitions and Bargaining Sets. J Math Econ 91:80\u201389","journal-title":"J Math Econ"},{"key":"780_CR16","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/0304-4068(86)90001-7","volume":"15","author":"J Greenberg","year":"1986","unstructured":"Greenberg J, Shitovitz B (1986) A simple proof of the equivalence theorem for oligopolistic mixed markets. J Math Econ 15:79\u201383","journal-title":"J Math Econ"},{"key":"780_CR17","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1016\/j.jmateco.2017.11.008","volume":"74","author":"C Herv\u00e9s-Beloso","year":"2018","unstructured":"Herv\u00e9s-Beloso C, Herv\u00e9s-Est\u00e9vez J, Moreno-Garc\u00eda E (2018) Bargaining sets in finite economies. J Math Econ 74:93\u201398","journal-title":"J Math Econ"},{"key":"780_CR18","doi-asserted-by":"crossref","unstructured":"Herv\u00e9s-Beloso C, Moreno-Garc\u00eda E (2001) The veto mechanism revisited. In: Lassonde M (ed) Approximation, optimization and mathematical economics. Phisica, Heidelberg, pp 147\u2013157","DOI":"10.1007\/978-3-642-57592-1_13"},{"key":"780_CR19","doi-asserted-by":"publisher","first-page":"697","DOI":"10.1016\/j.jmateco.2006.11.002","volume":"44","author":"C Herv\u00e9s-Beloso","year":"2008","unstructured":"Herv\u00e9s-Beloso C, Moreno-Garc\u00eda E (2008) Competitive equilibria and the grand coalition. J Math Econ 44:697\u2013706","journal-title":"J Math Econ"},{"key":"780_CR20","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1007\/s00182-014-0447-5","volume":"44","author":"J Herv\u00e9s-Est\u00e9vez","year":"2015","unstructured":"Herv\u00e9s-Est\u00e9vez J, Moreno-Garc\u00eda E (2015) On restricted bargaining sets. Int J Game Theory 44:631\u2013645","journal-title":"Int J Game Theory"},{"key":"780_CR21","doi-asserted-by":"crossref","unstructured":"Herv\u00e9s-Est\u00e9vez J, Moreno-Garc\u00eda E (2018a) A limit result on bargaining sets. Econ Theory 66:327\u2013341","DOI":"10.1007\/s00199-017-1063-y"},{"key":"780_CR22","doi-asserted-by":"crossref","unstructured":"Herv\u00e9s-Est\u00e9vez J, Moreno-Garc\u00eda E (2018b) Some equivalence results for a bargaining set in finite economies. Int J Econ Theory 14:129\u2013138","DOI":"10.1111\/ijet.12149"},{"key":"780_CR23","volume-title":"Core and equilibria of a large economy","author":"W Hildenbrand","year":"1974","unstructured":"Hildenbrand W (1974) Core and equilibria of a large economy. Princeton University Press, Princeton"},{"key":"780_CR24","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1016\/0304-4068(94)90029-9","volume":"23","author":"F H\u00fcsseinov","year":"1994","unstructured":"H\u00fcsseinov F (1994) Interpretation of Aubin\u2019s fuzzy coalitions and their extension. J Math Econ 23:499\u2013516","journal-title":"J Math Econ"},{"key":"780_CR25","unstructured":"H\u00fcsseinov F, Pascoa MR (1997) Fuzzy cores in production economics. FEUNL Working Paper Series, no. 298, pp. 1\u201321"},{"key":"780_CR26","doi-asserted-by":"publisher","first-page":"975","DOI":"10.1007\/s00182-014-0414-1","volume":"43","author":"J Liu","year":"2014","unstructured":"Liu J, Liu X (2014) Existence of Edgeworth and competitive equilibria and fuzzy cores in coalition production economies. Int J Game Theory 43:975\u2013990","journal-title":"Int J Game Theory"},{"key":"780_CR27","doi-asserted-by":"publisher","first-page":"1095","DOI":"10.1007\/s00182-015-0511-9","volume":"45","author":"J Liu","year":"2016","unstructured":"Liu J, Zhang H (2016) Coincidence of the Mas\u2013Colell bargaining set and the set of competitive equilibria in a continuum coalition production economy. Int J Game Theory 45:1095\u20131109","journal-title":"Int J Game Theory"},{"key":"780_CR28","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1016\/0304-4068(89)90017-7","volume":"18","author":"A Mas-Colell","year":"1989","unstructured":"Mas-Colell A (1989) An equivalence theorem for a bargaining set. J Math Econ 18:129\u2013139","journal-title":"J Math Econ"},{"key":"780_CR29","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1016\/S0304-4068(99)00036-1","volume":"34","author":"M Noguchi","year":"2000","unstructured":"Noguchi M (2000) A fuzzy core equivalence theorem. J Math Econ 34:143\u2013158","journal-title":"J Math Econ"},{"key":"780_CR30","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1016\/j.jmateco.2014.05.006","volume":"53","author":"M Pesce","year":"2014","unstructured":"Pesce M (2014) The veto mechanism in atomic differential information economies. J Math Econ 53:33\u201345","journal-title":"J Math Econ"},{"key":"780_CR31","doi-asserted-by":"publisher","first-page":"467","DOI":"10.2307\/1913371","volume":"41","author":"B Shitovitz","year":"1973","unstructured":"Shitovitz B (1973) Oligopoly in markets with a continuum of traders. Econometrica 41:467\u2013501","journal-title":"Econometrica"},{"key":"780_CR32","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1016\/0047-2727(82)90005-6","volume":"18","author":"W Thomson","year":"1982","unstructured":"Thomson W (1982) An informationally efficient equity criterion. J Public Econ 18:243\u2013263","journal-title":"J Public Econ"},{"key":"780_CR33","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1016\/0022-0531(88)90130-5","volume":"46","author":"W Thomson","year":"1988","unstructured":"Thomson W (1988) A study of choice correspondences in economies with a variable number of agents. J Econ Theory 46:237\u2013254","journal-title":"J Econ Theory"},{"key":"780_CR34","volume-title":"Handbook of social choice and welfare","author":"W Thomson","year":"2011","unstructured":"Thomson W (2011) Fair allocation rules. In: Arrow K, Sen A, Suzumura K (eds) Handbook of social choice and welfare. North-Holland, Amsterdam, New York"},{"key":"780_CR35","doi-asserted-by":"crossref","unstructured":"Thomson W, Zhou L (1993) Consistent solutions in atomless economies. Econometrica 61(3):575\u2013587","DOI":"10.2307\/2951718"},{"key":"780_CR36","doi-asserted-by":"crossref","unstructured":"Yang W, Liu J, Liu X (2011) Aubin cores and bargaining sets for convex cooperative fuzzy games. Int J Game Theory 40:467\u2013479","DOI":"10.1007\/s00182-010-0250-x"},{"key":"780_CR37","doi-asserted-by":"publisher","first-page":"158","DOI":"10.1016\/S0022-0531(05)80046-8","volume":"57","author":"L Zhou","year":"1992","unstructured":"Zhou L (1992) Strictly fair allocations in large exchange economies. J Econ Theory 57:158\u2013175","journal-title":"J Econ Theory"}],"container-title":["International Journal of Game Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00182-021-00780-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00182-021-00780-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00182-021-00780-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,4]],"date-time":"2023-11-04T11:52:56Z","timestamp":1699098776000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00182-021-00780-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,2]]},"references-count":37,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["780"],"URL":"https:\/\/doi.org\/10.1007\/s00182-021-00780-2","relation":{},"ISSN":["0020-7276","1432-1270"],"issn-type":[{"type":"print","value":"0020-7276"},{"type":"electronic","value":"1432-1270"}],"subject":[],"published":{"date-parts":[[2021,6,2]]},"assertion":[{"value":"9 May 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 June 2021","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}