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The Cooperative Game Theory of Networks and Hierarchies
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The Cooperative Game Theory of Networks and Hierarchies
von: Robert P. Gilles
Springer-Verlag, 2010
ISBN: 9783642052828
270 Seiten, Download: 2442 KB
 
Format:  PDF
geeignet für: Apple iPad, Android Tablet PC's PC, MAC, Laptop

Typ: B (paralleler Zugriff)

 

 
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Inhaltsverzeichnis

  Preface 6  
  Contents 10  
  List of Figures 12  
  1 Cooperative Game Theory 13  
     1.1 Aims and Outline of the Book 14  
     1.2 Game Forms 17  
        1.2.1 The Normal Form 19  
        1.2.2 The Characteristic Function Form 21  
     1.3 Cooperative Games 24  
        1.3.1 Basic Properties of Cooperative Games 25  
        1.3.2 The Standard Basis 26  
        1.3.3 The Unanimity Basis 27  
        1.3.4 Essential Games and Imputations 30  
     1.4 Multilinear Extensions 32  
     1.5 Problems 37  
  2 The Core of a Cooperative Game 40  
     2.1 Basic Properties of the Core 41  
        2.1.1 Representing the Core of a Three Player Game 42  
        2.1.2 The Core and Domination 46  
        2.1.3 Existence of Core Imputations 48  
     2.2 The Core Based on a Collection of Coalitions 50  
        2.2.1 Balanced Collections 56  
        2.2.2 Strongly Balanced Collections 58  
        2.2.3 Lattices and Hierarchies 59  
     2.3 Core Covers and Convex Games 62  
        2.3.1 The Weber Set 62  
        2.3.2 The Selectope 64  
     2.4 Appendix: Proofs of the Main Theorems 66  
     2.5 Problems 79  
  3 Axiomatic Value Theory 82  
     3.1 Equivalent Formulations of the Shapley Value 83  
     3.2 Three Axiomatizations of the Shapley Value 87  
        3.2.1 Shapley's Axiomatization 88  
        3.2.2 Young's Axiomatization 91  
        3.2.3 van den Brink's Axiomatization 93  
     3.3 The Shapley Value as a Utility Function 94  
     3.4 The Myerson Value 100  
     3.5 Appendix: Proofs of the Main Theorems 103  
     3.6 Problems 112  
  4 The Cooperative Potential 118  
     4.1 A Potential Function for Cooperative Games 119  
     4.2 The Cooperative Potential and the Shapley Value 123  
     4.3 Consistency and the Reductionist Approach 126  
     4.4 Beyond the Cooperative Potential 130  
        4.4.1 Value-Based Potentials 130  
        4.4.2 Share Functions and Share Potentials 133  
     4.5 Appendix: Proofs of the Main Theorems 137  
     4.6 Problems 149  
  5 Directed Communication Networks 154  
     5.1 Directed Networks 156  
     5.2 Measuring Dominance in Directed Networks 158  
        5.2.1 The Degree Measure 159  
        5.2.2 The ß-Measure 162  
        5.2.3 Iterated Power Measures 169  
     5.3 Hierarchical Allocation Rules on Network Games 174  
        5.3.1 Cooperative Network Situations 175  
        5.3.2 Network Myerson Values 177  
        5.3.3 The Hierarchical Payoff Property 179  
        5.3.4 The -Hierarchical Value 182  
     5.4 Appendix: Proofs of the Main Theorems 186  
     5.5 Problems 197  
  6 Cooperative Theories of Hierarchical Organizations 199  
     6.1 Games with a Permission Structure 201  
        6.1.1 The Conjunctive Approach 204  
        6.1.2 The Disjunctive Approach 208  
     6.2 Shapley Permission Values 220  
        6.2.1 The Conjunctive Permission Value 220  
        6.2.2 The Disjunctive Permission Value 226  
     6.3 Modeling Economic Phenomena 229  
     6.4 Appendix: Proofs of the Main Theorems 232  
     6.5 Discussion: More About the Disjunctive Restriction 247  
     6.6 Problems 249  
  References 254  
  Index 260  


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