{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T02:26:37Z","timestamp":1781490397052,"version":"3.54.1"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2018,3,9]],"date-time":"2018-03-09T00:00:00Z","timestamp":1520553600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71571143"],"award-info":[{"award-number":["71571143"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71671140"],"award-info":[{"award-number":["71671140"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","award":["201706290181"],"award-info":[{"award-number":["201706290181"]}],"id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2019,3]]},"DOI":"10.1007\/s10957-018-1259-8","type":"journal-article","created":{"date-parts":[[2018,3,9]],"date-time":"2018-03-09T11:33:21Z","timestamp":1520595201000},"page":"1065-1086","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["The Family of Ideal Values for Cooperative Games"],"prefix":"10.1007","volume":"180","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6173-7901","authenticated-orcid":false,"given":"Wenna","family":"Wang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hao","family":"Sun","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ren\u00e9","family":"van den Brink","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Genjiu","family":"Xu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2018,3,9]]},"reference":[{"key":"1259_CR1","first-page":"307","volume-title":"Contributions to the Theory of Games II, Annals of Mathematics Studies","author":"LS Shapley","year":"1953","unstructured":"Shapley, L.S.: A value for \n                    \n                      \n                    \n                    $$n$$\n                    \n                      \n                        n\n                      \n                    \n                  -person games. In: Kuhn, H.W., Tucker, A.W. (eds.) Contributions to the Theory of Games II, Annals of Mathematics Studies, pp. 307\u2013317. Princeton University Press, Princeton (1953)"},{"key":"1259_CR2","first-page":"317","volume":"19","author":"JF Banzhaf","year":"1965","unstructured":"Banzhaf, J.F.: Weighted voting doesn\u2019t work: a mathematical analysis. Rutgers Law Rev. 19, 317\u2013343 (1965)","journal-title":"Rutgers Law Rev."},{"key":"1259_CR3","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1007\/BF01753239","volume":"7","author":"J Deegan","year":"1978","unstructured":"Deegan, J., Packel, E.W.: A new index of power for simple \n                    \n                      \n                    \n                    $$n$$\n                    \n                      \n                        n\n                      \n                    \n                  -person games. Int. J. Game Theory 7, 113\u2013123 (1978)","journal-title":"Int. J. Game Theory"},{"key":"1259_CR4","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1016\/j.orl.2017.01.012","volume":"45","author":"W Wang","year":"2017","unstructured":"Wang, W., Sun, H., Xu, G., Hou, D.: Procedural interpretation and associated consistency for the egalitarian Shapley values. Oper. Res. Lett. 45, 164\u2013169 (2017)","journal-title":"Oper. Res. Lett."},{"key":"1259_CR5","doi-asserted-by":"publisher","first-page":"1163","DOI":"10.1137\/0117107","volume":"17","author":"D Schmeidler","year":"1969","unstructured":"Schmeidler, D.: The nucleolus of a characteristic function game. SIAM J. Appl. Math. 17, 1163\u20131170 (1969)","journal-title":"SIAM J. Appl. Math."},{"key":"1259_CR6","first-page":"151","volume":"6","author":"AI Sobolev","year":"1975","unstructured":"Sobolev, A.I.: The characterization of optimality principles in cooperative games by functional equations. Math. Methods Soc. Sci. 6, 151\u2013153 (1975)","journal-title":"Math. Methods Soc. Sci."},{"key":"1259_CR7","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1007\/BF01254388","volume":"25","author":"LM Ruiz","year":"1996","unstructured":"Ruiz, L.M., Valenciano, F., Zarzuelo, J.M.: The least square prenucleolus and the least square nucleolus. Two values for TU games based on the excess vector. Int. J. Game Theory 25, 113\u2013134 (1996)","journal-title":"Int. J. Game Theory"},{"key":"1259_CR8","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1006\/game.1997.0622","volume":"24","author":"LM Ruiz","year":"1998","unstructured":"Ruiz, L.M., Valenciano, F., Zarzuelo, J.M.: The family of least square values for transferable utility games. Games Econ. Behav. 24, 109\u2013130 (1998)","journal-title":"Games Econ. Behav."},{"issue":"1","key":"1259_CR9","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/BF02564802","volume":"6","author":"LM Ruiz","year":"1998","unstructured":"Ruiz, L.M., Valenciano, F., Zarzuelo, J.M.: Some new results on least square values for TU games. Top 6(1), 139\u2013158 (1998)","journal-title":"Top"},{"key":"1259_CR10","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1016\/j.orl.2014.11.001","volume":"43","author":"TD Nguyen","year":"2015","unstructured":"Nguyen, T.D.: The fairest core in cooperative games with transferable utilities. Oper. Res. Lett. 43, 34\u201339 (2015)","journal-title":"Oper. Res. Lett."},{"key":"1259_CR11","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1007\/s00182-010-0222-1","volume":"30","author":"TSH Driessen","year":"2010","unstructured":"Driessen, T.S.H.: Associated consistency and values for TU games. Int. J. Game Theory 30, 467\u2013482 (2010)","journal-title":"Int. J. Game Theory"},{"key":"1259_CR12","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1007\/s00182-012-0361-7","volume":"42","author":"M Malawski","year":"2013","unstructured":"Malawski, M.: Procedural values for cooperative games. Int. J. Game Theory 42, 305\u2013324 (2013)","journal-title":"Int. J. Game Theory"},{"key":"1259_CR13","doi-asserted-by":"publisher","first-page":"551","DOI":"10.1007\/s00182-005-0217-5","volume":"33","author":"Y Hwang","year":"2005","unstructured":"Hwang, Y., Li, J., Hsiao, Y.: A dynamic approach to the Shapley value based on associated games. Int. J. Game Theory 33, 551\u2013562 (2005)","journal-title":"Int. J. Game Theory"},{"key":"1259_CR14","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1016\/j.orl.2016.12.004","volume":"45","author":"Y Hwang","year":"2017","unstructured":"Hwang, Y., Liao, Y.: Alternative formulation and dynamic process for the efficient Banzhaf\u2013Owen index. Oper. Res. Lett. 45, 60\u201362 (2017)","journal-title":"Oper. Res. Lett."},{"key":"1259_CR15","doi-asserted-by":"publisher","first-page":"15C30","DOI":"10.1007\/BF01719767","volume":"13","author":"TSH Driessen","year":"1991","unstructured":"Driessen, T.S.H., Funaki, F.: Coincidence of and collinearity between game theoretic solutions. OR Spektrum 13, 15C30 (1991)","journal-title":"OR Spektrum"},{"key":"1259_CR16","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1016\/0022-0531(85)90082-1","volume":"36","author":"H Moulin","year":"1985","unstructured":"Moulin, H.: The separability axiom and equal sharing method. J. Econ. Theory 36, 120\u2013148 (1985)","journal-title":"J. Econ. Theory"},{"key":"1259_CR17","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1007\/s11238-007-9083-x","volume":"67","author":"R Brink van den","year":"2009","unstructured":"van den Brink, R., Funaki, Y.: Axiomatizations of a class of equal surplus sharing solutions for TU-games. Theory Decis. 67, 303\u2013340 (2009)","journal-title":"Theory Decis."},{"key":"1259_CR18","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1007\/s001820100080","volume":"30","author":"G Hamiache","year":"2001","unstructured":"Hamiache, G.: Associated consistency and Shapley value. Int. J. Game Theory 30, 279\u2013289 (2001)","journal-title":"Int. J. Game Theory"},{"key":"1259_CR19","doi-asserted-by":"publisher","first-page":"709","DOI":"10.1007\/s00199-005-0640-7","volume":"28","author":"Y Hwang","year":"2006","unstructured":"Hwang, Y.: Associated consistency and equal allocation of nonseparable costs. Econ. Theory 28, 709\u2013719 (2006)","journal-title":"Econ. Theory"},{"key":"1259_CR20","doi-asserted-by":"publisher","first-page":"826","DOI":"10.1016\/j.orl.2016.10.008","volume":"44","author":"Y Hwang","year":"2016","unstructured":"Hwang, Y., Wang, B.: A matrix approach to the associated consistency with respect to the equal allocation of non-separable costs. Oper. Res. Lett. 44, 826\u2013830 (2016)","journal-title":"Oper. Res. Lett."},{"key":"1259_CR21","doi-asserted-by":"publisher","first-page":"2205","DOI":"10.1016\/j.laa.2013.06.026","volume":"439","author":"G Xu","year":"2013","unstructured":"Xu, G., Wang, W., Hou, D.: Axiomatization for the center-of-gravity of imputation set value. Linear Algebra Appl. 439, 2205\u20132215 (2013)","journal-title":"Linear Algebra Appl."},{"key":"1259_CR22","doi-asserted-by":"publisher","first-page":"224","DOI":"10.1016\/j.laa.2014.12.036","volume":"471","author":"G Xu","year":"2015","unstructured":"Xu, G., van den Brink, R., van der Laan, G., Sun, H.: Associated consistency characterization of two linear values for TU games by matrix approach. Linear Algebra Appl. 471, 224\u2013240 (2015)","journal-title":"Linear Algebra Appl."},{"issue":"05","key":"1259_CR23","doi-asserted-by":"publisher","first-page":"1550031","DOI":"10.1142\/S0217595915500311","volume":"32","author":"G Xu","year":"2015","unstructured":"Xu, G., Dai, H., Shi, H.: Axiomatizations and a noncooperative interpretation of the \n                    \n                      \n                    \n                    $$\\alpha $$\n                    \n                      \n                        \u03b1\n                      \n                    \n                  -CIS value. Asia Pac. J. Oper. Res. 32(05), 1550031 (2015)","journal-title":"Asia Pac. J. Oper. Res."},{"key":"1259_CR24","unstructured":"Joosten, R.: Dynamics, equilibria and values. Ph.D. dissertation, Maastricht University (1996)"},{"key":"1259_CR25","doi-asserted-by":"publisher","first-page":"693","DOI":"10.1007\/s00355-011-0634-2","volume":"40","author":"R Brink van den","year":"2013","unstructured":"van den Brink, R., Funaki, Y., Ju, Y.: Reconciling marginalism with egalitarianism: consistency, monotonicity, and implementation of egalitarian Shapley values. Soc. Choice Welf. 40, 693\u2013714 (2013)","journal-title":"Soc. Choice Welf."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-018-1259-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-018-1259-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-018-1259-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,8]],"date-time":"2019-03-08T19:40:46Z","timestamp":1552074046000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-018-1259-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,9]]},"references-count":25,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,3]]}},"alternative-id":["1259"],"URL":"https:\/\/doi.org\/10.1007\/s10957-018-1259-8","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,9]]},"assertion":[{"value":"9 January 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 February 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 March 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}