{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T04:05:36Z","timestamp":1759032336572},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2010,10,27]],"date-time":"2010-10-27T00:00:00Z","timestamp":1288137600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int J Game Theory"],"published-print":{"date-parts":[[2011,8]]},"DOI":"10.1007\/s00182-010-0258-2","type":"journal-article","created":{"date-parts":[[2010,10,26]],"date-time":"2010-10-26T13:40:14Z","timestamp":1288100414000},"page":"617-630","source":"Crossref","is-referenced-by-count":6,"title":["A new class of convex games on \u03c3-algebras and the optimal partitioning of measurable spaces"],"prefix":"10.1007","volume":"40","author":[{"given":"Nobusumi","family":"Sagara","sequence":"first","affiliation":[]},{"given":"Milan","family":"Vlach","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2010,10,27]]},"reference":[{"key":"258_CR1","volume-title":"Values of non-atomic games","author":"RJ Aumann","year":"1974","unstructured":"Aumann RJ, Shapley LS (1974) Values of non-atomic games. Princeton University Press, Princeton"},{"key":"258_CR2","first-page":"119","volume":"10","author":"ON Bondareva","year":"1963","unstructured":"Bondareva ON (1963) Some applications of linear programming methods to the theory of cooperative games. Problemy Kibernitiki 10: 119\u2013139 (in Russian)","journal-title":"Problemy Kibernitiki"},{"key":"258_CR3","doi-asserted-by":"crossref","first-page":"363","DOI":"10.2307\/30037474","volume":"112","author":"M Dall\u2019Aglio","year":"2005","unstructured":"Dall\u2019Aglio M, Maccheroni F (2005) Fair division without additivity. Am Math Mon 112: 363\u2013365","journal-title":"Am Math Mon"},{"key":"258_CR4","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/0022-247X(74)90133-4","volume":"45","author":"F Delbaen","year":"1974","unstructured":"Delbaen F (1974) Convex games and extreme points. J Math Anal Appl 45: 210\u2013233","journal-title":"J Math Anal Appl"},{"key":"258_CR5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/2311357","volume":"68","author":"LE Dubins","year":"1961","unstructured":"Dubins LE, Spanier EH (1961) How to cut a cake fairly. Am Math Mon 68: 1\u201317","journal-title":"Am Math Mon"},{"key":"258_CR6","volume-title":"Linear operators, Part I: General theory","author":"N Dunford","year":"1958","unstructured":"Dunford N, Schwartz JT (1958) Linear operators, Part I: General theory. Wiley, New York"},{"key":"258_CR7","doi-asserted-by":"crossref","first-page":"59","DOI":"10.2140\/pjm.1951.1.59","volume":"1","author":"A Dvoretsky","year":"1951","unstructured":"Dvoretsky A, Wald A, Wolfowitz J (1951) Relations among certain ranges of vector measures. Pac J Math 1: 59\u201374","journal-title":"Pac J Math"},{"key":"258_CR8","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-9440-2","volume-title":"Measure theory","author":"PR Halmos","year":"1950","unstructured":"Halmos PR (1950) Measure theory. Van Nostrand, New York"},{"key":"258_CR9","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1007\/s00182-008-0124-7","volume":"37","author":"F H\u00fcsseinov","year":"2008","unstructured":"H\u00fcsseinov F (2008) Existence of the core in a heterogeneous divisible commodity exchange economy. Int J Game Theory 37: 387\u2013395","journal-title":"Int J Game Theory"},{"key":"258_CR10","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1006\/game.1999.0820","volume":"36","author":"JM Izqueirdo","year":"2001","unstructured":"Izqueirdo JM, Rafels C (2001) Average monotonic cooperative games. Games Econ Behav 36: 174\u2013192","journal-title":"Games Econ Behav"},{"key":"258_CR11","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/0022-247X(69)90044-4","volume":"27","author":"Y Kannai","year":"1969","unstructured":"Kannai Y (1969) Countably additive measures in cores of games. J Math Anal Appl 27: 227\u2013240","journal-title":"J Math Anal Appl"},{"key":"258_CR12","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/S1574-0005(05)80015-3","volume-title":"Handbook of game theory with economic applications, vol 1","author":"Y Kannai","year":"1992","unstructured":"Kannai Y (1992) The core and balancedness. In: Aumann RJ, Hart S (eds) Handbook of game theory with economic applications, vol 1. Elsevier, Amsterdam, pp 355\u2013395"},{"key":"258_CR13","doi-asserted-by":"crossref","first-page":"1165","DOI":"10.2140\/pjm.1959.9.1165","volume":"9","author":"JL Kelley","year":"1959","unstructured":"Kelley JL (1959) Measures on Boolean algebras. Pac J Math 9: 1165\u20131177","journal-title":"Pac J Math"},{"key":"258_CR14","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/0022-247X(85)90177-5","volume":"109","author":"J Legut","year":"1985","unstructured":"Legut J (1985) The problem of fair division for countably many participants. J Math Anal Appl 109: 83\u201389","journal-title":"J Math Anal Appl"},{"key":"258_CR15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01769272","volume":"15","author":"J Legut","year":"1986","unstructured":"Legut J (1986) Market games with a continuum of indivisible commodities. Int J Game Theory 15: 1\u20137","journal-title":"Int J Game Theory"},{"key":"258_CR16","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1007\/s003550200192","volume":"20","author":"F Maccheroni","year":"2003","unstructured":"Maccheroni F, Marinacci M (2003) How to cut a pizza fairly: fair division with decreasing marginal evaluations. Soc Choice Welf 20: 457\u2013465","journal-title":"Soc Choice Welf"},{"key":"258_CR17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0304-4068(02)00080-0","volume":"39","author":"M Marinacci","year":"2003","unstructured":"Marinacci M, Montrucchio L (2003) Subcalculus for set functions and cores of TU games. J Math Econ 39: 1\u201325","journal-title":"J Math Econ"},{"key":"258_CR18","doi-asserted-by":"crossref","first-page":"46","DOI":"10.4324\/9780203358061_chapter_4","volume-title":"Uncertainty in economic theory","author":"M Marinacci","year":"2004","unstructured":"Marinacci M, Montrucchio L (2004) Introduction to the mathematics of ambiguity. In: Gilboa I (ed) Uncertainty in economic theory. Routledge, New York, pp 46\u2013107"},{"key":"258_CR19","first-page":"475","volume":"42","author":"N Sagara","year":"2006","unstructured":"Sagara N (2006) An existence result on partitioning of a measurable space: Pareto optimality and core. Kybernetika 42: 475\u2013481","journal-title":"Kybernetika"},{"key":"258_CR20","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/j.mathsocsci.2007.09.007","volume":"55","author":"N Sagara","year":"2008","unstructured":"Sagara N (2008) A characterization of \u03b1-maximin solutions of fair division problems. Math Soc Sci 55: 273\u2013280","journal-title":"Math Soc Sci"},{"key":"258_CR21","unstructured":"Sagara N (2010) Fair division problems with nonadditive evaluations: existence of solutions and representation of preference orderings. In: Varela J, Acu\u00f1a S (eds) Handbook of optimization theory: decision analysis and application. Nova Science Publishers, Hauppauge (forthcoming)"},{"key":"258_CR22","doi-asserted-by":"crossref","first-page":"624","DOI":"10.1016\/j.fss.2008.09.009","volume":"160","author":"N Sagara","year":"2009","unstructured":"Sagara N, Vlach M (2009) Representation of preference relations on \u03c3-algebras of nonatomic measure spaces: convexity and continuity. Fuzzy Sets Syst 160: 624\u2013634","journal-title":"Fuzzy Sets Syst"},{"key":"258_CR23","first-page":"89","volume":"6","author":"N Sagara","year":"2010","unstructured":"Sagara N, Vlach M (2010a) Convex functions on \u03c3-algebras of nonatomic measure spaces. Pac J Optim 6: 89\u2013102","journal-title":"Pac J Optim"},{"key":"258_CR24","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/978-4-431-99490-9_6","volume":"6","author":"N Sagara","year":"2010","unstructured":"Sagara N, Vlach M (2010b) Convexity of the lower partition range of a concave vector measure. Adv Math Econ 6: 155\u2013160","journal-title":"Adv Math Econ"},{"key":"258_CR25","doi-asserted-by":"crossref","first-page":"50","DOI":"10.2307\/1909383","volume":"35","author":"HE Scarf","year":"1967","unstructured":"Scarf HE (1967) The core of an N person game. Econometrica 35: 50\u201369","journal-title":"Econometrica"},{"key":"258_CR26","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1016\/0022-247X(72)90045-5","volume":"40","author":"D Schmeidler","year":"1972","unstructured":"Schmeidler D (1972) Cores of exact games, I. J Math Anal Appl 40: 214\u2013225","journal-title":"J Math Anal Appl"},{"key":"258_CR27","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1002\/nav.3800140404","volume":"14","author":"LS Shapley","year":"1967","unstructured":"Shapley LS (1967) On balanced sets and cores. Naval Res Logist 14: 453\u2013460","journal-title":"Naval Res Logist"},{"key":"258_CR28","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/BF01753431","volume":"1","author":"LS Shapley","year":"1971","unstructured":"Shapley LS (1971) Cores of convex games. Int J Game Theory 1: 11\u201326","journal-title":"Int J Game Theory"},{"key":"258_CR29","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/0022-0531(69)90008-8","volume":"1","author":"LS Shapley","year":"1969","unstructured":"Shapley LS, Shubik M (1969) On market games. J Econ Theory 1: 9\u201325","journal-title":"J Econ Theory"}],"container-title":["International Journal of Game Theory"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00182-010-0258-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00182-010-0258-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00182-010-0258-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T18:40:48Z","timestamp":1558636848000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00182-010-0258-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,10,27]]},"references-count":29,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2011,8]]}},"alternative-id":["258"],"URL":"https:\/\/doi.org\/10.1007\/s00182-010-0258-2","relation":{},"ISSN":["0020-7276","1432-1270"],"issn-type":[{"value":"0020-7276","type":"print"},{"value":"1432-1270","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,10,27]]}}}