{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T03:37:19Z","timestamp":1780630639564,"version":"3.54.1"},"publisher-location":"Berlin, Heidelberg","reference-count":39,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642322402","type":"print"},{"value":"9783642322419","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012]]},"DOI":"10.1007\/978-3-642-32241-9_48","type":"book-chapter","created":{"date-parts":[[2012,8,13]],"date-time":"2012-08-13T15:12:12Z","timestamp":1344870732000},"page":"568-579","source":"Crossref","is-referenced-by-count":19,"title":["Computing Shapley Value in Supermodular Coalitional Games"],"prefix":"10.1007","author":[{"given":"David","family":"Liben-Nowell","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexa","family":"Sharp","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tom","family":"Wexler","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kevin","family":"Woods","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"key":"48_CR1","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1016\/S0899-8256(03)00176-3","volume":"47","author":"A. Archer","year":"2004","unstructured":"Archer, A., Feigenbaum, J., Krishnamurthy, A., Sami, R., Shenker, S.: Approximation and collusion in multicast cost sharing. Games and Economic Behavior\u00a047, 36\u201371 (2004)","journal-title":"Games and Economic Behavior"},{"key":"48_CR2","unstructured":"Aziz, H.: Algorithmic and complexity aspects of simple coalitional games. PhD thesis, University of Warwick (2009)"},{"key":"48_CR3","doi-asserted-by":"crossref","unstructured":"Bachrach, Y., Markakis, E., Resnick, E., Procaccia, A.D., Rosenschein, J.S., Saberi, A.: Approximating power indices: theoretical and empirical analysis. In: Autonomous Agents and Multi-Agent Systems, vol.\u00a020, pp. 105\u2013122 (2010)","DOI":"10.1007\/s10458-009-9078-9"},{"key":"48_CR4","first-page":"317","volume":"19","author":"J.F. Banzhaf","year":"1965","unstructured":"Banzhaf, J.F.: Weighted voting doesn\u2019t work: A mathematical analysis. Rutgers Law Review\u00a019, 317\u2013343 (1965)","journal-title":"Rutgers Law Review"},{"key":"48_CR5","unstructured":"Barua, R., Chakravarty, S.R., Roy, S.: Measuring power in weighted majority games. Technical report. Department of Economics, Iowa State University (2007)"},{"issue":"5","key":"48_CR6","doi-asserted-by":"publisher","first-page":"1170","DOI":"10.1086\/228631","volume":"92","author":"P. Bonacich","year":"1987","unstructured":"Bonacich, P.: Power and centrality: A family of measures. American Journal of Sociology\u00a092(5), 1170\u20131182 (1987)","journal-title":"American Journal of Sociology"},{"issue":"1\u20137","key":"48_CR7","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1016\/S0169-7552(98)00110-X","volume":"30","author":"S. Brin","year":"1998","unstructured":"Brin, S., Page, L.: The anatomy of a large-scale hypertextual Web search engine. Computer Networks and ISDN Systems\u00a030(1\u20137), 107\u2013117 (1998)","journal-title":"Computer Networks and ISDN Systems"},{"key":"48_CR8","first-page":"143","volume":"31","author":"I.J. Curiel","year":"1987","unstructured":"Curiel, I.J., Maschler, M., Tijs, S.: Bankruptcy games. Zeitschrift f\u00fcr Operations Research\u00a031, 143\u2013159 (1987)","journal-title":"Zeitschrift f\u00fcr Operations Research"},{"key":"48_CR9","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1002\/nav.3800120303","volume":"12","author":"M. Davis","year":"1965","unstructured":"Davis, M., Maschler, M.: The kernel of a cooperative game. Naval Research Logistics Quarterly\u00a012, 223\u2013259 (1965)","journal-title":"Naval Research Logistics Quarterly"},{"issue":"2","key":"48_CR10","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-person games. International Journal of Game Theory\u00a07(2), 113\u2013123 (1978)","journal-title":"International Journal of Game Theory"},{"issue":"1","key":"48_CR11","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1007\/978-0-387-77247-9_7","volume":"17","author":"X. Deng","year":"2008","unstructured":"Deng, X., Fang, Q.: Algorithmic cooperative game theory. Pareto Optimality, Game Theory and Equilibria\u00a017(1), 159\u2013185 (2008)","journal-title":"Pareto Optimality, Game Theory and Equilibria"},{"issue":"2","key":"48_CR12","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1287\/moor.19.2.257","volume":"19","author":"X. Deng","year":"1994","unstructured":"Deng, X., Papadimitriou, C.: On the complexity of cooperative solution concepts. Mathematics of Operations Research\u00a019(2), 257\u2013266 (1994)","journal-title":"Mathematics of Operations Research"},{"key":"48_CR13","doi-asserted-by":"crossref","unstructured":"Fatima, S.S., Wooldridge, M., Jennings, N.R.: A randomized method for the Shapley value for the voting game. In: Proc.\u00a06th Conference on Autonomous Agents and Multiagent Systems, pp. 955\u2013962 (May 2007)","DOI":"10.1145\/1329125.1329316"},{"issue":"14","key":"48_CR14","doi-asserted-by":"publisher","first-page":"1673","DOI":"10.1016\/j.artint.2008.05.003","volume":"172","author":"S.S. Fatima","year":"2008","unstructured":"Fatima, S.S., Wooldridge, M., Jennings, N.R.: A linear approximation method for the Shapley value. Artificial Intelligence\u00a0172(14), 1673\u20131699 (2008)","journal-title":"Artificial Intelligence"},{"key":"48_CR15","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1006\/jcss.2001.1754","volume":"63","author":"J. Feigenbaum","year":"2001","unstructured":"Feigenbaum, J., Papadimitriou, C., Shenker, S.: Sharing the cost of multicast transmissions. J. Computing Systems Sciences\u00a063, 21\u201341 (2001)","journal-title":"J. Computing Systems Sciences"},{"issue":"3-4","key":"48_CR16","first-page":"373","volume":"102","author":"D. Felsenthal","year":"2000","unstructured":"Felsenthal, D., Machover, M.: The measurement of voting power: Theory and practice, problems and paradoxes. Public Choice\u00a0102(3-4), 373\u2013376 (2000)","journal-title":"Public Choice"},{"key":"48_CR17","first-page":"47","volume":"4","author":"D.B. Gillies","year":"1959","unstructured":"Gillies, D.B.: Solutions to general non-zero-sum games. Contributions to the Theory of Games\u00a04, 47\u201385 (1959)","journal-title":"Contributions to the Theory of Games"},{"key":"48_CR18","doi-asserted-by":"publisher","first-page":"847","DOI":"10.1109\/90.650144","volume":"5","author":"S. Herzog","year":"1997","unstructured":"Herzog, S., Shenker, S., Estrin, D.: Sharing the \u201ccost\u201d of multicast trees: an axiomatic analysis. IEEE\/ACM Transactions on Networking\u00a05, 847\u2013860 (1997)","journal-title":"IEEE\/ACM Transactions on Networking"},{"key":"48_CR19","doi-asserted-by":"crossref","unstructured":"Ieong, S., Shoham, Y.: Marginal contribution nets: a compact representation scheme for coalitional games. In: Proc. 6th ACM Conference on Electronic Commerce (2005)","DOI":"10.1145\/1064009.1064030"},{"key":"48_CR20","doi-asserted-by":"crossref","unstructured":"Iwata, S., Fleischer, L., Fujishige, S.: A combinatorial, strongly polynomial-time algorithm for minimizing submodular functions. In: Proc.\u00a032nd Symposium on Theory of Computing, pp. 97\u2013106 (2000)","DOI":"10.1145\/335305.335317"},{"key":"48_CR21","doi-asserted-by":"crossref","unstructured":"Jain, K., Vazirani, V.: Applications of approximation algorithms to cooperative games. In: Proc. 33rd ACM Symposium on Theory of Computing (2001)","DOI":"10.1145\/380752.380825"},{"issue":"1","key":"48_CR22","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1007\/BF02289026","volume":"18","author":"L. Katz","year":"1953","unstructured":"Katz, L.: A new status index derived from sociometric analysis. Psychometrika\u00a018(1), 39\u201343 (1953)","journal-title":"Psychometrika"},{"key":"48_CR23","doi-asserted-by":"crossref","unstructured":"Kleinberg, J., Tardos, E.: Balanced outcomes in social exchange networks. In: Proc.\u00a040th Symposium on Theory of Computing (2008)","DOI":"10.1145\/1374376.1376994"},{"issue":"1","key":"48_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1111\/1467-9248.00356","volume":"50","author":"D. Leech","year":"2002","unstructured":"Leech, D.: An empirical comparison of the performance of classical power indices. Political Studies\u00a050(1), 1\u201322 (2002)","journal-title":"Political Studies"},{"key":"48_CR25","unstructured":"Mann, I., Shapley, L.S.: Values of large games, IV: Evaluating the electoral college by Monte-Carlo techniques. Technical report. The Rand Corporation, Santa Monica, CA (1960)"},{"key":"48_CR26","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/BF01753435","volume":"1","author":"M. Maschler","year":"1971","unstructured":"Maschler, M., Peleg, B., Shapley, L.S.: The kernel and bargaining set for convex games. International Journal of Game Theory\u00a01, 73\u201393 (1971)","journal-title":"International Journal of Game Theory"},{"issue":"4","key":"48_CR27","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1287\/moor.4.4.303","volume":"4","author":"M. Maschler","year":"1979","unstructured":"Maschler, M., Peleg, B., Shapley, L.S.: Geometric properties of the kernel, nucleolus, and related solution concepts. Mathematics of Operations Research\u00a04(4), 303\u2013338 (1979)","journal-title":"Mathematics of Operations Research"},{"issue":"1","key":"48_CR28","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/S0453-4514(00)88752-9","volume":"43","author":"Y. Matsui","year":"2000","unstructured":"Matsui, Y., Matsui, T.: A survey of algorithms for calculating power indices of weighted majority games. Journal of the Operations Research Society of Japan\u00a043(1), 71\u201386 (2000)","journal-title":"Journal of the Operations Research Society of Japan"},{"issue":"1-2","key":"48_CR29","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1016\/S0304-3975(00)00251-6","volume":"263","author":"Y. Matsui","year":"2001","unstructured":"Matsui, Y., Matsui, T.: NP-completeness for calculating power indices of weighted majority games. Theoretical Computer Science\u00a0263(1-2), 305\u2013310 (2001)","journal-title":"Theoretical Computer Science"},{"key":"48_CR30","doi-asserted-by":"crossref","unstructured":"Motwani, R., Raghavan, P.: Randomized Algorithms, Cambridge (1995)","DOI":"10.1017\/CBO9780511814075"},{"issue":"4","key":"48_CR31","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1016\/0165-4896(82)90029-4","volume":"2","author":"B. O\u2019Neill","year":"1982","unstructured":"O\u2019Neill, B.: A problem of rights arbitration from the Talmud. Mathematical Social Sciences\u00a02(4), 345\u2013371 (1982)","journal-title":"Mathematical Social Sciences"},{"key":"48_CR32","doi-asserted-by":"publisher","first-page":"346","DOI":"10.1006\/jctb.2000.1989","volume":"80","author":"A. Schrijver","year":"2000","unstructured":"Schrijver, A.: A combinatorial algorithm minimizing submodular functions in strongly polynomial time. Journal of Combinatorial Theory B\u00a080, 346\u2013355 (2000)","journal-title":"Journal of Combinatorial Theory B"},{"key":"48_CR33","unstructured":"Schulz, A.S., Uhan, N.A.: Approximating the least core value and least core of cooperative games with supermodular costs. Working paper (2010)"},{"issue":"4","key":"48_CR34","doi-asserted-by":"publisher","first-page":"1051","DOI":"10.1287\/opre.1100.0841","volume":"58","author":"A.S. Schulz","year":"2010","unstructured":"Schulz, A.S., Uhan, N.A.: Sharing supermodular costs. Operations Research\u00a058(4), 1051\u20131056 (2010)","journal-title":"Operations Research"},{"key":"48_CR35","doi-asserted-by":"crossref","unstructured":"Shapley, L.S.: A value for n-person games. In: Kuhn, H., Tucker, A.W. (eds.) Contributions to the Theory of Games II, pp. 307\u2013317. Princeton University Press (1953)","DOI":"10.1515\/9781400881970-018"},{"key":"48_CR36","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1007\/BF01753431","volume":"1","author":"L.S. Shapley","year":"1971","unstructured":"Shapley, L.S.: Cores of convex games. International Journal of Game Theory\u00a01, 11\u201326 (1971)","journal-title":"International Journal of Game Theory"},{"key":"48_CR37","first-page":"678","volume":"59","author":"L.S. Shapley","year":"1969","unstructured":"Shapley, L.S., Shubik, M.: On the core of an economic system with externalities. American Economic Review\u00a059, 678\u2013684 (1969)","journal-title":"American Economic Review"},{"issue":"2","key":"48_CR38","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1287\/opre.26.2.305","volume":"26","author":"D.M. Topkis","year":"1978","unstructured":"Topkis, D.M.: Minimizing a submodular function on a lattice. Operations Research\u00a026(2), 305\u2013321 (1978)","journal-title":"Operations Research"},{"key":"48_CR39","doi-asserted-by":"crossref","unstructured":"Yao, A.C.: Probabilistic computations: Toward a unified measure of complexity. In: Proc.\u00a018th Symposium on Foundations of Computer Science, pp. 222\u2013227 (1977)","DOI":"10.1109\/SFCS.1977.24"}],"container-title":["Lecture Notes in Computer Science","Computing and Combinatorics"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-32241-9_48.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,24]],"date-time":"2020-11-24T03:09:40Z","timestamp":1606187380000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-32241-9_48"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"ISBN":["9783642322402","9783642322419"],"references-count":39,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-32241-9_48","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012]]}}}