The Cooperative Game Theory of Networks and Hierarchies

Online-Ressource (XI, 270p. 40 illus., 20 illus. in color, digital)

Theory and Decision Library C, Game Theory, Mathematical Programming and Operations Research ; 44

Literaturverz. S. 245 - 249

Preface; Contents; List of Figures; to 1 Cooperative Game Theory; 1.1 Aims and Outline of the Book; 1.2 Game Forms; 1.2.1 The Normal Form; 1.2.2 The Characteristic Function Form; 1.3 Cooperative Games; 1.3.1 Basic Properties of Cooperative Games; 1.3.2 The Standard Basis; 1.3.3 The Unanimity Basis; 1.3.4 Essential Games and Imputations; 1.4 Multilinear Extensions; 1.5 Problems; to 2 The Core of a Cooperative Game; 2.1 Basic Properties of the Core; 2.1.1 Representing the Core of a Three Player Game; 2.1.2 The Core and Domination; 2.1.3 Existence of Core Imputations

2.2 The Core Based on a Collection of Coalitions2.2.1 Balanced Collections; 2.2.2 Strongly Balanced Collections; 2.2.3 Lattices and Hierarchies; 2.3 Core Covers and Convex Games; 2.3.1 The Weber Set; 2.3.2 The Selectope; 2.4 Appendix: Proofs of the Main Theorems; 2.5 Problems; to 3 Axiomatic Value Theory; 3.1 Equivalent Formulations of the Shapley Value; 3.2 Three Axiomatizations of the Shapley Value; 3.2.1 Shapley's Axiomatization; 3.2.2 Young's Axiomatization; 3.2.3 van den Brink's Axiomatization; 3.3 The Shapley Value as a Utility Function; 3.4 The Myerson Value

3.5 Appendix: Proofs of the Main Theorems3.6 Problems; to 4 The Cooperative Potential; 4.1 A Potential Function for Cooperative Games; 4.2 The Cooperative Potential and the Shapley Value; 4.3 Consistency and the Reductionist Approach; 4.4 Beyond the Cooperative Potential; 4.4.1 Value-Based Potentials; 4.4.2 Share Functions and Share Potentials; 4.5 Appendix: Proofs of the Main Theorems; 4.6 Problems; to 5 Directed Communication Networks; 5.1 Directed Networks; 5.2 Measuring Dominance in Directed Networks; 5.2.1 The Degree Measure; 5.2.2 The β-Measure

5.2.3 Iterated Power Measures5.3 Hierarchical Allocation Rules on Network Games; 5.3.1 Cooperative Network Situations; 5.3.2 Network Myerson Values; 5.3.3 The Hierarchical Payoff Property; 5.3.4 The -Hierarchical Value; 5.4 Appendix: Proofs of the Main Theorems; 5.5 Problems; to 6 Cooperative Theories of Hierarchical Organizations; 6.1 Games with a Permission Structure; 6.1.1 The Conjunctive Approach; 6.1.2 The Disjunctive Approach; 6.2 Shapley Permission Values; 6.2.1 The Conjunctive Permission Value; 6.2.2 The Disjunctive Permission Value; 6.3 Modeling Economic Phenomena

6.4 Appendix: Proofs of the Main Theorems6.5 Discussion: More About the Disjunctive Restriction; 6.6 Problems; References; Index;

10.1007/978-3-642-05282-8 [DOI]

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