On the Nucleolus of a Characteristic Function Game

Previous article Next article On the Nucleolus of a Characteristic Function GameElon KohlbergElon Kohlberghttps://doi.org/10.1137/0120009PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] David Schmeidler, The nucleolus of a characteristic function game, SIAM J. Appl. Math., 17 (1969), 1163–1170 10.1137/0117107 MR0260432 0191.49502 LinkISIGoogle Scholar[2] J. Farkas, Über die Theorie der einfachen Ungleichungen, J. Reine Angew. Math., 124 (1901), 1–27 Google Scholar[3] L. S. Shapley, On balanced sets and cores, Naval Res. Logist. Quart., 14 (1967), 453–460 CrossrefGoogle Scholar[4] A. Charnes and , K. O. Kortanek, On classes of convex and preemptive nuclei for n-person games, Tech. Rep., 31, Operations Research Dept., Cornell University, Ithaca, N.Y., 1967 Google Scholar[5] A. Charnes and , K. O. Kortanek, On asymptotic behavior of some nuclei of n-person games and the piecewise linearity of the nucleolus, Management Sci. Res. Rep., 170, Grad. School of Ind. Adm., Carnegie–Mellon University, Pittsburgh, Penn., 1969 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails The nucleolus and inheritance of properties in communication situations25 March 2022 | Annals of Operations Research, Vol. 54 Cross Ref An Adaptive Model of Demand Adjustment in Weighted Majority Games26 December 2021 | Games, Vol. 13, No. 1 Cross Ref Finding and verifying the nucleolus of cooperative games6 June 2020 | Mathematical Programming, Vol. 190, No. 1-2 Cross Ref Computationally Efficient Pricing and Benefit Distribution Mechanisms for Incentivizing Stable Peer-to-Peer Energy TradingIEEE Internet of Things Journal, Vol. 8, No. 2 Cross Ref Contention Resolution, Matrix Scaling and Fair Allocation1 January 2022 Cross Ref The impact of Nord Stream 2 on the European gas market bargaining positionsEnergy Policy, Vol. 144 Cross Ref Monotonicity and Weighted Prenucleoli: A Characterization Without ConsistencyMathematics of Operations Research, Vol. 45, No. 3 Cross Ref Valuations and dynamics of negotiations19 November 2019 | Journal of Public Economic Theory, Vol. 22, No. 1 Cross Ref Weighted nucleoli and dually essential coalitions10 June 2019 | International Journal of Game Theory, Vol. 48, No. 4 Cross Ref Synergy within the West African Triple Helix innovation systems as measured with game theoryJournal of Industry-University Collaboration, Vol. 1, No. 2 Cross Ref The Nucleolus and Inheritance of Properties in Communication SituationsSSRN Electronic Journal Cross Ref Modelling the Triple Helix of university-industry-government relationships with game theory: Core, Shapley value and nucleolus as indicators of synergy within an innovation systemJournal of Informetrics, Vol. 12, No. 4 Cross Ref Az adósságelengedés modellezése kooperatív játékelmélettelKözgazdasági Szemle, Vol. 65, No. 7-8 Cross Ref The SD-Prenucleolus for TU-Games: Coalitional Monotonicity and Core Stability22 September 2017 Cross Ref Monotonicity and Weighted Prenucleoli: A Characterization Without ConsistencySSRN Electronic Journal Cross Ref Game Theory15 February 2018 Cross Ref On the 1-nucleolus24 June 2017 | Mathematical Methods of Operations Research, Vol. 86, No. 2 Cross Ref Coincidence of the Shapley value with other solutions satisfying covarianceMathematical Social Sciences, Vol. 89 Cross Ref Characterizations of highway toll pricing methodsEuropean Journal of Operational Research, Vol. 260, No. 1 Cross Ref The General Nucleolus of n-Person Cooperative Games14 October 2017 Cross Ref A monotonic core solution for convex TU games10 September 2015 | International Journal of Game Theory, Vol. 45, No. 4 Cross Ref Axiomatizations of symmetrically weighted solutions12 November 2013 | Annals of Operations Research, Vol. 243, No. 1-2 Cross Ref Characterization sets for the nucleolus in balanced gamesOperations Research Letters, Vol. 44, No. 4 Cross Ref Characterizations of solutions for games with precedence constraints31 January 2015 | International Journal of Game Theory, Vol. 45, No. 1-2 Cross Ref Characterizations of the core of TU and NTU games with communication structures29 September 2015 | Social Choice and Welfare, Vol. 46, No. 2 Cross Ref Finding the nucleoli of large cooperative gamesEuropean Journal of Operational Research, Vol. 248, No. 3 Cross Ref Cooperative Game Theoretic Approach21 June 2016 Cross Ref Bankruptcy and the per capita nucleolus: The claim-and-right rules familyMathematical Social Sciences, Vol. 77 Cross Ref The Nucleolus Cross Ref On Highway ProblemsSSRN Electronic Journal Cross Ref The SD-prenucleolus for TU games2 November 2014 | Mathematical Methods of Operations Research, Vol. 80, No. 3 Cross Ref Understanding the coincidence of allocation rules: symmetry and orthogonality in TU-games16 January 2014 | International Journal of Game Theory, Vol. 43, No. 4 Cross Ref Factors that influence cooperation in networks for innovation and learningComputers in Human Behavior, Vol. 37 Cross Ref On extensions of the core and the anticore of transferable utility games3 March 2013 | International Journal of Game Theory, Vol. 43, No. 1 Cross Ref The Positive Core for Games with Precedence ConstraintsSSRN Electronic Journal Cross Ref Game theoretic analysis of maximum cooperative purchasing situations16 October 2013 | Naval Research Logistics (NRL), Vol. 60, No. 8 Cross Ref The prenucleolus and the prekernel for games with communication structures30 June 2013 | Mathematical Methods of Operations Research, Vol. 78, No. 2 Cross Ref The prenucleolus for games with restricted cooperationMathematical Social Sciences, Vol. 66, No. 1 Cross Ref Consortium Formation Using a Consensus Policy Based Negotiation Framework Cross Ref On the Nucleolus as a Power Index19 March 2013 Cross Ref Bankruptcy and the Per Capita NucleolusSSRN Electronic Journal Cross Ref Nonsymmetric variants of the prekernel and the prenucleolus10 July 2011 | International Journal of Game Theory, Vol. 41, No. 4 Cross Ref Aggregate monotonic stable single-valued solutions for cooperative games30 October 2012 | International Journal of Game Theory, Vol. 41, No. 4 Cross Ref Minimal exact balancednessMathematical Social Sciences, Vol. 64, No. 2 Cross Ref Dynamic game model with strategic element on cooperation and confront Cross Ref Excess based allocation of risk capitalInsurance: Mathematics and Economics, Vol. 50, No. 1 Cross Ref Interaction between Dutch Soccer Teams and Fans: A Mathematical Analysis through Cooperative Game TheoryApplied Mathematics, Vol. 03, No. 01 Cross Ref A polynomial time algorithm for computing the nucleolus for a class of disjunctive games with a permission structure11 November 2010 | International Journal of Game Theory, Vol. 40, No. 3 Cross Ref On Chinese postman games where residents of each road pay the cost of their roadGames and Economic Behavior, Vol. 72, No. 2 Cross Ref The monoclus of a coalitional gameGames and Economic Behavior, Vol. 71, No. 2 Cross Ref On the coincidence propertyGames and Economic Behavior, Vol. 71, No. 2 Cross Ref On 1-convexity and nucleolus of co-insurance gamesInsurance: Mathematics and Economics, Vol. 48, No. 2 Cross Ref Games on Union Closed SystemsSSRN Electronic Journal Cross Ref Cores of combined gamesJournal of Economic Theory, Vol. 145, No. 6 Cross Ref The nucleolus of a standard tree game revisited: a study of its monotonicity and computational properties10 September 2009 | International Journal of Game Theory, Vol. 39, No. 1-2 Cross Ref The positive core of a cooperative game21 November 2009 | International Journal of Game Theory, Vol. 39, No. 1-2 Cross Ref A simulation for content-based and utility-based recommendation of candidate coalitions in virtual creativity teamsProcedia Computer Science, Vol. 1, No. 2 Cross Ref Between the Prekernel and the PrenucleolusSSRN Electronic Journal Cross Ref The Prenucleolus for Games with a Restricted CooperationSSRN Electronic Journal Cross Ref Excess Based Allocation of Risk CapitalSSRN Electronic Journal Cross Ref Remarks on a surplus-sharing rule from the Mishneh Torah14 February 2009 | TOP, Vol. 17, No. 2 Cross Ref On the coincidence of the prenucleolus and the Shapley valueMathematical Social Sciences, Vol. 57, No. 1 Cross Ref FAIR ALLOCATION BASED ON TWO CRITERIA : A DEA GAME VIEW OF "ADD THEM UP AND DIVIDE BY TWO"(Operations Research for Performance Evaluation)Journal of the Operations Research Society of Japan, Vol. 52, No. 2 Cross Ref Cores of Combined GamesSSRN Electronic Journal Cross Ref An axiomatic approach to egalitarianism in TU-games2 July 2008 | International Journal of Game Theory, Vol. 37, No. 4 Cross Ref A MODIFIED KOHLBERG CRITERION AND A NONLINEAR METHOD TO COMPUTE THE NUCLEOLUS OF A COOPERATIVE GAMETaiwanese Journal of Mathematics, Vol. 12, No. 6 Cross Ref Game Theory22 March 2017 Cross Ref The Monoclus of a Coalitional GameSSRN Electronic Journal Cross Ref Proportional Payoffs in Majority GamesSSRN Electronic Journal Cross Ref Computation of the Nucleolus for a Class of Disjunctive Games with a Permission StructureSSRN Electronic Journal Cross Ref An Algorithm for Computing the Nucleolus of Disjunctive Additive Games with an Acyclic Permission StructureSSRN Electronic Journal Cross Ref A Distributed Algorithm for Finding Nucleolus-Stable Payoff Divisions Cross Ref A COMPUTATIONAL APPROACH TO THE COINCIDENCE OF EGALITARIAN SOLUTIONS FOR COST-SHARING GAMES20 November 2011 | International Game Theory Review, Vol. 08, No. 01 Cross Ref Noncooperative foundations of the nucleolus in majority gamesGames and Economic Behavior, Vol. 54, No. 2 Cross Ref Monotonicity properties of the nucleolus on the domain of veto balanced gamesTop, Vol. 13, No. 2 Cross Ref Mergers and Acquisitions: An Experimental Analysis of Synergies, Externalities and DynamicsEuropean Finance Review, Vol. 8, No. 4 Cross Ref Cartels via the modiclusDiscrete Applied Mathematics, Vol. 134, No. 1-3 Cross Ref Valuations and Dynamics of NegotiationsSSRN Electronic Journal Cross Ref Consistency, converse consistency, and aspirations in TU-gamesMathematical Social Sciences, Vol. 45, No. 3 Cross Ref Reconfirming the PrenucleolusMathematics of Operations Research, Vol. 28, No. 2 Cross Ref On the nucleolus of neighbor gamesEuropean Journal of Operational Research, Vol. 146, No. 1 Cross Ref Equal Treatment for Both Sides of Assignment Games in the Modified Least Core Cross Ref Game Theory 1950–2000 Cross Ref Individual rights and collective responsibility: the rights–egalitarian solutionMathematical Social Sciences, Vol. 37, No. 1 Cross Ref Orderings, excess functions, and the nucleolusMathematical Social Sciences, Vol. 36, No. 2 Cross Ref Axiomatizations of Game Theoretical Solutions for One-Output Cost Sharing ProblemsGames and Economic Behavior, Vol. 24, No. 1-2 Cross Ref The B-Nucleolus of TU-GamesGames and Economic Behavior, Vol. 24, No. 1-2 Cross Ref A Characterization of the Nucleolus for Convex GamesGames and Economic Behavior, Vol. 23, No. 1 Cross Ref The modified nucleolus: Properties and axiomatizationsInternational Journal of Game Theory, Vol. 26, No. 2 Cross Ref The nucleolus and kernel of veto-rich transferable utility gamesInternational Journal of Game Theory, Vol. 26, No. 1 Cross Ref On aspiration solutions in predicting coalition formation in cooperative gamesApplied Mathematics, Vol. 11, No. 4 Cross Ref A simple procedure to compute the nucleolus of Γ-component additive gamesTop, Vol. 3, No. 2 Cross Ref The nucleolus for cooperative games with arbitrary bounds of individual rationalityInternational Journal of Game Theory, Vol. 24, No. 1 Cross Ref ?-component additive gamesInternational Journal of Game Theory, Vol. 24, No. 1 Cross Ref The nucleolus of homogeneous games with stepsDiscrete Applied Mathematics, Vol. 50, No. 1 Cross Ref On the Locus of the Nucleolus Cross Ref The least core, nucleolus, and kernel of homogeneous weighted majority gamesGames and Economic Behavior, Vol. 4, No. 4 Cross Ref The general nucleolus and the reduced game propertyInternational Journal of Game Theory, Vol. 21, No. 1 Cross Ref Lexicographic optimality in the multiple objective linear programming: The nucleolar solutionEuropean Journal of Operational Research, Vol. 57, No. 3 Cross Ref Chapter 18 The bargaining set, kernel, and nucleolus Cross Ref On finding the nucleolus of an n-person cooperative gameInternational Journal of Game Theory, Vol. 19, No. 4 Cross Ref An axiomatization of the nucleolusInternational Journal of Game Theory, Vol. 19, No. 4 Cross Ref A comparison of lambda-transfer and core solutions in constant-sum non-sidepayment gamesBehavioral Science, Vol. 36, No. 2 Cross Ref Extensions of Value Solutions in Constant-Sum Non-Sidepayment Games1 July 2016 | Journal of Conflict Resolution, Vol. 33, No. 3 Cross Ref Comparative accuracy of value solutions in non-sidepayment games with empty coreTheory and Decision, Vol. 26, No. 3 Cross Ref Game Theory Cross Ref Analysis of an ecological nicheMathematical Biosciences, Vol. 87, No. 1 Cross Ref A test of the characteristic function and the Harsanyi function in N-person normal form sidepayment gamesTheory and Decision, Vol. 23, No. 2 Cross Ref Continuity properties of solution concepts for cooperative games1 June 1987 | Operations-Research-Spektrum, Vol. 9, No. 2 Cross Ref Remarks on the reasonable set of outcomes in a general coalition function form gameInternational Journal of Game Theory, Vol. 16, No. 2 Cross Ref Computation of the nucleolus of some bilateral market gamesInternational Journal of Game Theory, Vol. 16, No. 1 Cross Ref Game Theory10 November 2016 Cross Ref Solution concepts ofk-convexn-person gamesInternational Journal of Game Theory, Vol. 15, No. 4 Cross Ref Mollifier Representation in Non-Constant-Sum Games1 July 2016 | Journal of Conflict Resolution, Vol. 30, No. 2 Cross Ref The τ-value, The core and semiconvex gamesInternational Journal of Game Theory, Vol. 14, No. 4 Cross Ref Game theoretic analysis of a bankruptcy problem from the TalmudJournal of Economic Theory, Vol. 36, No. 2 Cross Ref A Procedure for Computing the f-Nucleolus of a Cooperative Game Cross Ref On the predictive efficiency of the core solution in side-payment gamesTheory and Decision, Vol. 15, No. 1 Cross Ref On the regions of linearity for the nucleolus and their computationInternational Journal of Game Theory, Vol. 12, No. 1 Cross Ref A competitive test of the core solution in side-payment gamesBehavioral Science, Vol. 27, No. 1 Cross Ref Coincidence of k-and n-kernels for centered gamesLithuanian Mathematical Journal, Vol. 22, No. 1 Cross Ref A procedure for finding the nucleolus of a cooperativen person gameZeitschrift für Operations Research, Vol. 25, No. 5 Cross Ref On the comparative accuracy of lexicographical solutions in cooperative gamesInternational Journal of Game Theory, Vol. 10, No. 2 Cross Ref Nonsymmetry and Core Size in N-Person Sidepayment Games1 July 2016 | Journal of Conflict Resolution, Vol. 24, No. 3 Cross Ref Effects of core properties in four-person games with side-paymentsBehavioral Science, Vol. 24, No. 4 Cross Ref Iterative processes with "nucleolar" restrictionsInternational Journal of Game Theory, Vol. 6, No. 4 Cross Ref A generalization of theKohlberg criterionInternational Journal of Game Theory, Vol. 6, No. 4 Cross Ref Characterization of the nucleolus for a class ofn-person gamesNaval Research Logistics Quarterly, Vol. 24, No. 3 Cross Ref Optimality and Dynamics in Coalitional Games Cross Ref Economically Efficient and Politically Sustainable Economic Contraction Cross Ref The Cost Assignment of the Cooperative Water Resource Development Cross Ref Domination structures and multicriteria problems in n-person gamesTheory and Decision, Vol. 8, No. 1 Cross Ref The nucleolus and kernel for simple games or special valid inequalities for 0–1 linear integer programsInternational Journal of Game Theory, Vol. 5, No. 4 Cross Ref Extending the Nucleolus to Infinite Player GamesCharles Bird12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 31, No. 3AbstractPDF (986 KB)Coalitional and Chance-Constrained Solutions to n-Person Games. I: The Prior Satisficing NucleolusA. Charnes and Daniel Granot12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 31, No. 2AbstractPDF (848 KB)Dynamics of cooperative gamesInternational Journal of Game Theory, Vol. 5, No. 1 Cross Ref Excess Functions for Cooperative Games without SidepaymentsEhud Kalai12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 29, No. 1AbstractPDF (1076 KB)Cooperative games with coalition structuresInternational Journal of Game Theory, Vol. 3, No. 4 Cross Ref On the Nonmonotonicity of the Bargaining Set, the Kernel and the Nucleolus of GameNimrod Megiddo12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 27, No. 2AbstractPDF (352 KB)The Nucleolus as a Solution of a Minimization ProblemElon Kohlberg12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 23, No. 1AbstractPDF (495 KB)The kernel and bargaining set for convex gamesInternational Journal of Game Theory, Vol. 1, No. 1 Cross Ref Observations on the nucleolus and the central gameInternational Journal of Game Theory, Vol. 1, No. 1 Cross Ref Some Recent Developments in n-Person Game TheoryW. F. Lucas18 July 2006 | SIAM Review, Vol. 13, No. 4AbstractPDF (3775 KB)Surplus-Sharing Local Games in Dynamic Exchange Processes Cross Ref Volume 20, Issue 1| 1971SIAM Journal on Applied Mathematics History Submitted:11 November 1969Published online:12 July 2006 InformationCopyright © 1971 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0120009Article page range:pp. 62-66ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics