Introduction to the Theory of Cooperative Games. ( = Theory and Decision Library/ C: Game Theory, Mathematical Programming and Operations Research, 34) . - hardcover

EAN (ISBN-13): 9781402074103
ISBN (ISBN-10): 1402074107
Hardcover
Publishing year: 2003
Publisher: Springer

Book in our database since 2007-05-27T07:35:46+01:00 (London)
Detail page last modified on 2023-10-14T17:53:07+01:00 (London)
ISBN/EAN: 1402074107

ISBN - alternate spelling:
1-4020-7410-7, 978-1-4020-7410-3
Alternate spelling and related search-keywords:
Book author: bezalel peleg, sudholt
Book title: introduction theory cooperative games, introduction the theory games, introduction decision theory, theory and decision library, introduction operations research, mathematical game theory, mathematical programming

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Information from Publisher

Author: Bezalel Peleg; Peter Sudhölter
Title: Theory and Decision Library C; Introduction to the Theory of Cooperative Games
Publisher: Springer; Springer US
380 Pages
Publishing year: 2003-05-31
New York; NY; US
Weight: 0,735 kg
Language: English
85,55 € (DE)
87,95 € (AT)
106,60 CHF (CH)
Not available, publisher indicates OP

BB; Book; Hardcover, Softcover / Wirtschaft/Volkswirtschaft; Wirtschaftstheorie und -philosophie; CON_D023P; C; Economic Theory/Quantitative Economics/Mathematical Methods; Economics and Finance; Game Theory, Economics, Social and Behav. Sciences; Operations Research/Decision Theory; Spieltheorie; Unternehmensforschung; Management: Entscheidungstheorie; BC; EA

1 Introduction.- 1.1 Cooperative Games.- 1.2 Outline of the Book.- 1.2.1 TU Games.- 1.2.2 NTU Games.- 1.2.3 A Guide for the Reader.- 1.3 Special Remarks.- 1.3.1 Axiomatizations.- 1.3.2 Interpersonal Comparisons of Utility.- 1.3.3 Nash’s Program.- I TU Games.- 2 Coalitional TU Games and Solutions.- 2.1 Coalitional Games.- 2.2 Some Families of Games.- 2.2.1 Market Games.- 2.2.2 Cost Allocation Games.- 2.2.3 Simple Games.- 2.3 Properties of Solutions.- 2.4 Notes and Comments.- 3 The Core.- 3.1 The Bondareva-Shapley Theorem.- 3.2 An Application to Market Games.- 3.3 Totally Balanced Games.- 3.4 Some Families of Totally Balanced Games.- 3.4.1 Minimum Cost Spanning Tree Games.- 3.4.2 Permutation Games.- 3.5 A Characterization of Convex Games.- 3.6 An Axiomatization of the Core.- 3.7 An Axiomatization of the Core on Market Games.- 3.8 The Core for Games with Various Coalition Structures.- 3.9 Notes and Comments.- 4 Bargaining Sets.- 4.1 The Bargaining Set M.- 4.2 Existence of the Bargaining Set.- 4.3 Balanced Superadditive Games and the Bargaining Set.- 4.4 Further Bargaining Sets.- 4.4.1 The Reactive and the Semi-Reactive Bargaining Set.- 4.4.2 The Mas-Colell Bargaining Set.- 4.5 Non-Monotonicity of Bargaining Sets.- 4.6 The Bargaining Set and Syndication: An Example.- 4.7 Notes and Comments.- 5 The Prekernel, Kernel, and Nucleolus.- 5.1 The Nucleolus and the Prenucleolus.- 5.2 The Reduced Game Property.- 5.3 Desirability, Equal Treatment, and the Prekernel.- 5.4 An Axiomatization of the Prekernel.- 5.5 Individual Rationality and the Kernel.- 5.6 Reasonableness of the Prekernel and the Kernel.- 5.7 The Prekernel of a Convex Game.- 5.8 The Prekernel and Syndication.- 5.9 Notes and Comments.- 6 The Prenucleolus.- 6.1 A Combinatorial Characterization of the Prenucleolus.- 6.2 Preliminary Results.- 6.3 An Axiomatization of the Prenucleolus.- 6.3.1 An Axiomatization of the Nucleolus.- 6.3.2 The Positive Core.- 6.4 The Prenucleolus of Games with Coalition Structures.- 6.5 The Nucleolus of Strong Weighted Majority Games.- 6.6 The Modiclus.- 6.6.1 Constant-Sum Games.- 6.6.2 Convex Games.- 6.6.3 Weighted Majority Games.- 6.7 Notes and Comments.- 7 Geometric Properties of the ?-Core. Kernel, and Prekernel.- 7.1 Geometric Properties of the ?-Core.- 7.2 Some Properties of the Least-Core.- 7.3 The Reasonable Set.- 7.4 Geometric Characterizations of the Prekernel and Kernel.- 7.5 A Method for Computing the Prenucleolus.- 7.6 Notes and Comments.- 8 The Shapley Value.- 8.1 Existence and Uniqueness of the Value.- 8.2 Monotonicity Properties of Solutions and the Value.- 8.3 Consistency.- 8.4 The Potential of the Shapley Value.- 8.5 A Reduced Game for the Shapley Value.- 8.6 The Shapley Value for Simple Games.- 8.7 Games with Coalition Structures.- 8.8 Games with a priori Unions.- 8.9 Multilinear Extensions of Games.- 8.10 Notes and Comments.- 8.11 A Summary of some Properties of the Main Solutions.- 9 Continuity Properties of Solutions.- 9.1 Upper Hemicontinuity of Solutions.- 9.2 Lower Hemicontinuity of Solutions.- 9.3 Continuity of the Prenucleolus.- 9.4 Notes and Comments.- 10 Dynamic Bargaining Procedures for the Kernel.- 10.1 Dynamic Systems for the Kernel and the Bargaining Set.- 10.2 Stable Sets of the Kernel and the Bargaining Set.- 10.3 Asymptotic Stability of the Nucleolus.- 10.4 Notes and Comments.- II NTU Games.- 11 Cooperative Games in Strategic and Coalitional Form.- 11.1 Cooperative Games in Strategic Form.- 11.2 ?- and ?-Effectiveness.- 11.3 Coalitional Games with Nontransferable Utility.- 11.4 Cooperative Games with Side Payments but without TU.- 11.5 Notes and Comments.- 12 The Core of NTU Games.- 12.1 Individual Rationality, Pareto Optimality, and the Core.- 12.2 Balanced NTU Games.- 12.3 Ordinal and Cardinal Convex Games.- 12.3.1 Ordinal Convex Games.- 12.3.2 Cardinal Convex Games.- 12.4 An Axiomatization of the Core.- 12.4.1 Reduced Games of NTU Games.- 12.4.2 Axioms for the Core.- 12.4.3 Proof of Theorem 12.4..- 12.5 Additional Properties and Characterizations.- 12.6 Notes and Comments.- 13 Some Values of NTU Games.- 13.1 The Shapley Value of NTU Games.- 13.2 A Characterization of the Shapley NTU Value.- 13.3 The Harsanyi Solution.- 13.4 The Consistent Shapley Value.- 13.5 Notes and Comments.- 14 Bargaining Sets for NTU Games.- 14.1 The Bargaining Set M.- 14.2 The Ordinal Bargaining Set M°.- 14.3 A Proof of Billera’s Theorem.- 14.4 Solutions Related to M°.- 14.4.1 The Ordinal (Semi-)Reactive Bargaining Set.- 14.4.2 Solutions Related to the Prekernel.- 14.5 Notes and Comments.