{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T08:38:11Z","timestamp":1775119091173,"version":"3.50.1"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[1995,6,1]],"date-time":"1995-06-01T00:00:00Z","timestamp":801964800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ZOR - Methods and Models of Operations Research"],"published-print":{"date-parts":[[1995,6]]},"DOI":"10.1007\/bf01415753","type":"journal-article","created":{"date-parts":[[2005,4,3]],"date-time":"2005-04-03T19:27:19Z","timestamp":1112556439000},"page":"189-216","source":"Crossref","is-referenced-by-count":27,"title":["Directed and weighted majority games"],"prefix":"10.1007","volume":"42","author":[{"given":"I.","family":"Krohn","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"Sudh\ufffdlter","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"CR1","first-page":"531","volume":"19","author":"RJ Aumann","year":"1965","unstructured":"Aumann RJ, Peleg B, Rabinowitz P (1965) A method for computing the kernel ofn-person games. Mathematics of Computation 19:531?551","journal-title":"Mathematics of Computation"},{"key":"CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4540-7","volume-title":"Mathematical introduction to linear programming and game theory","author":"L Brickmann","year":"1989","unstructured":"Brickmann L (1989) Mathematical introduction to linear programming and game theory. Springer-Verlag New York"},{"key":"CR3","unstructured":"Dubey P, Shapley LS (1978) Mathematical properties of the banzhaf power index. The Rand Corporation 99-31"},{"key":"CR4","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/0165-4896(85)90032-0","volume":"10","author":"E Einy","year":"1985","unstructured":"Einy E (1985) The desirability relation of simple games. Math Social Sc 10:155?168","journal-title":"Math Social Sc"},{"key":"CR5","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/BF01268159","volume":"18","author":"E Einy","year":"1989","unstructured":"Einy E, Lehrer E (1989) Regular simple games. Int Journal of Game Theory 18:195?208","journal-title":"Int Journal of Game Theory"},{"key":"CR6","volume-title":"Sperner theory in partially ordered sets","author":"K Engel","year":"1985","unstructured":"Engel K, Gronau HD (1985) Sperner theory in partially ordered sets. Teubner Verlag Leipzig"},{"key":"CR7","doi-asserted-by":"crossref","unstructured":"Erd\u00f6s P (1965) Extremal problems in number theory. Theory of numbers. Whiteman AL (Ed) Amer Math Soc Proc Symp Pure Math 8:181?189","DOI":"10.1090\/pspum\/008\/0174539"},{"key":"CR8","unstructured":"Euler L (1750) De partitione numerorum. Commentationes Arithmeticae"},{"key":"CR9","doi-asserted-by":"crossref","first-page":"21","DOI":"10.2307\/2002191","volume":"13","author":"JR Isbell","year":"1959","unstructured":"Isbell JR (1959) On the enumeraton of majority games. Math Tables Aids Comput 13:21?28","journal-title":"Math Tables Aids Comput"},{"key":"CR10","unstructured":"Kopelowitz A (1967) Computation of the kernel of simple games and the nucleolus ofn-person games. Research program in game theory and math economics. Dept of Math The Hebrew University of Jerusalem RM 31"},{"key":"CR11","doi-asserted-by":"crossref","first-page":"289","DOI":"10.2140\/pjm.1966.18.289","volume":"18","author":"M Maschler","year":"1966","unstructured":"Maschler M, Peleg B (1966) A characterization, existence proof and dimension bounds for the kernel of a game. Pacific J Math 18:289?328","journal-title":"Pacific J Math"},{"key":"CR12","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1287\/moor.4.4.303","volume":"4","author":"M Maschler","year":"1979","unstructured":"Maschler M, Peleg B, Shapley LS (1979) Geometric properties of the kernel, nucleolus and related solution concepts. Math of Operations Research 4:303?338","journal-title":"Math of Operations Research"},{"key":"CR13","volume-title":"Theory of games and economic behavior","author":"J Neumann von","year":"1944","unstructured":"von Neumann J, Morgenstern O (1944) Theory of games and economic behavior. Princeton University Press New Jersey"},{"key":"CR14","unstructured":"Ostmann A (1987) Life-length of a process with elements of decreasing importance. Working Paper 156 Inst of Math ec University of Bielefeld"},{"key":"CR15","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/BF01756245","volume":"16","author":"A Ostmann","year":"1987","unstructured":"Ostmann A (1987a) On the minimal representation of homogeneous games. Int Journal of Game Theory 16:69?81","journal-title":"Int Journal of Game Theory"},{"key":"CR16","unstructured":"Ostmann A (1989) Simple games: On order and Symmetrie. Working Paper 169 Inst of Math University of Bielefeld"},{"key":"CR17","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1137\/0116042","volume":"16","author":"B Peleg","year":"1968","unstructured":"Peleg B (1968) On weights of constant-sum majority games. SIAM J of Appl Math 16:527?532","journal-title":"SIAM J of Appl Math"},{"key":"CR18","doi-asserted-by":"crossref","first-page":"588","DOI":"10.1016\/0899-8256(92)90039-U","volume":"4","author":"B Peleg","year":"1992","unstructured":"Peleg B, Rosenm\u00fcller J (1992) The least-core, nucleolus, and kernel of homogeneous weighted majority games. Games and Economic Behaviour 4:588?605","journal-title":"Games and Economic Behaviour"},{"key":"CR19","doi-asserted-by":"crossref","unstructured":"Peleg B, Rosenm\u00fcller J, Sudh\u00f6lter P (1994) The kernel of homogeneous games with steps. Essays in game theory in honor of Michael Maschler, Jerusalem. Nimrod M (ed) 163?192","DOI":"10.1007\/978-1-4612-2648-2_13"},{"key":"CR20","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1137\/0603026","volume":"3","author":"RA Proctor","year":"1982","unstructured":"Proctor RA (1982a) Representations of sl (2, ?) on posets and the sperner property. SIAM J Algebraic Discrete Methods 3:275?280","journal-title":"SIAM J Algebraic Discrete Methods"},{"key":"CR21","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1080\/00029890.1982.11995524","volume":"89","author":"RA Proctor","year":"1982","unstructured":"Proctor RA (1982b) Solution of two difficult combinatorial problems with linear algebra. The American Mathematical Monthly 89:721?734","journal-title":"The American Mathematical Monthly"},{"key":"CR22","unstructured":"Rosenm\u00fcller J (1981) The theory of games and markets. North Holland Publ Comp"},{"key":"CR23","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1287\/moor.12.2.309","volume":"12","author":"Rosenm\u00fcller","year":"1987","unstructured":"Rosenm\u00fcller (1987) Homogeneous games: Recursive structure and computation. Math of Operations Research 12:309?330","journal-title":"Math of Operations Research"},{"key":"CR24","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/0166-218X(94)90163-5","volume":"50","author":"J Rosenm\u00fcller","year":"1994","unstructured":"Rosenm\u00fcller J, Sudh\u00f6lter P (1994) The nucleolus of homogeneous games with steps. Discrete Applied Mathematics 50:53?76","journal-title":"Discrete Applied Mathematics"},{"key":"CR25","unstructured":"Schmeidler D (1966) The nucleolus of a characteristic function game. Research program in game theory and math economics. The Hebrew University of Jerusalem RM 23"},{"key":"CR26","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1002\/bs.3830070104","volume":"7","author":"LS Shapley","year":"1962","unstructured":"Shapley LS (1962) Simple games: An outline of the descriptive theory. Behavioral Sci 7:59?66","journal-title":"Behavioral Sci"},{"key":"CR27","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1137\/0601021","volume":"1","author":"RP Stanley","year":"1980","unstructured":"Stanley RP (1980) Weyl groups, the hard lefschetz theorem, and the sperner property. SIAM J Algebraic Discrete Methods 1:168?184","journal-title":"SIAM J Algebraic Discrete Methods"},{"key":"CR28","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1007\/BF01358803","volume":"18","author":"P Sudh\u00f6lter","year":"1989","unstructured":"Sudh\u00f6lter P (1989) Homogeneous games as anti step functions. Int Journal of Game Theory 18: 433?469","journal-title":"Int Journal of Game Theory"},{"key":"CR29","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/BF01761605","volume":"5","author":"LA Wolsey","year":"1976","unstructured":"Wolsey LA (1976) The nucleolus and kernel of simple games or special valid inequalities for 0?1 linear integer programs. Int Journal of Game Theory 5:227?238","journal-title":"Int Journal of Game Theory"}],"container-title":["ZOR Zeitschrift f\ufffdr Operations Research Methods and Models of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01415753.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01415753\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01415753","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,6]],"date-time":"2020-04-06T17:26:20Z","timestamp":1586193980000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01415753"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,6]]},"references-count":29,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1995,6]]}},"alternative-id":["BF01415753"],"URL":"https:\/\/doi.org\/10.1007\/bf01415753","relation":{},"ISSN":["0340-9422","1432-5217"],"issn-type":[{"value":"0340-9422","type":"print"},{"value":"1432-5217","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,6]]}}}