Introduction to the Theory of Cooperative Games

Transcription

1 Bezalel Peleg Peter Sudholter Introduction to the Theory of Cooperative Games Second Edition 4y Springer

2 Preface to the Second Edition Preface to the First Edition List of Figures List of Tables Notation and Symbols V VI XIII XV XVII 1 Introduction Cooperative Games Outline of the Book TU Games NTU Games A Guide for the Reader Special Remarks Axiomatizations Interpersonal Comparisons of Utility Nash's Program 6 Part I TU Games 2 Coalitional TU Games and Solutions Coalitional Games 9

3 VIII 2.2 Some Families of Games Market Games Cost Allocation Games Simple Games Properties of Solutions Notes and Comments 26 3 The Core The Bondareva-Shapley Theorem An Application to Market Games Totally Balanced Games Some Families of Totally Balanced Games Minimum Cost Spanning Tree Games Permutation Games A Characterization of Convex Games An Axiomatization of the Core An Axiomatization of the Core on Market Games The Core for Games with Various Coalition Structures Notes and Comments 48 4 Bargaining Sets The Bargaining Set M Existence of the Bargaining Set Balanced Superadditive Games and the Bargaining Set Further Bargaining Sets The Reactive and the Semi-reactive Bargaining Set The Mas-Colell Bargaining Set Non-monotonicity of Bargaining Sets The Bargaining Set and Syndication: An Example Notes and Comments 79

4 IX 5 The Prekernel, Kernel, and Nucleolus The Nucleolus and the Prenucleolus The Reduced Game Property Desirability, Equal Treatment, and the Prekernel An Axiomatization of the Prekernel Individual Rationality and the Kernel Reasonableness of the Prekernel and the Kernel The Prekernel of a Convex Game The Prekernel and Syndication Notes and Comments The Prenucleolus A Combinatorial Characterization of the Prenucleolus Preliminary Results An Axiomatization of the Prenucleolus An Axiomatization of the Nucleolus The Positive Core The Prenucleolus of Games with Coalition Structures The Nucleolus of Strong Weighted Majority Games The Modiclus Constant-Sum Games Convex Games Weighted Majority Games Notes and Comments Geometric Properties of the e-core, Kernel, and Prekernel Geometric Properties of the e-core Some Properties of the Least-Core The Reasonable Set Geometric Characterizations of the Prekernel and Kernel A Method for Computing the Prenucleolus Notes and Comments 149

5 X 8 The Shapley Value Existence and Uniqueness of the Value Monotonicity Properties of Solutions and the Value Consistency The Potential of the Shapley Value A Reduced Game for the Shapley Value The Shapley Value for Simple Games Games with Coalition Structures Games with A Priori Unions Multilinear Extensions of Games Notes and Comments A Summary of Some Properties of the Main Solutions Continuity Properties of Solutions Upper Hemicontinuity of Solutions Lower Hemicontinuity of Solutions Continuity of the Prenucleolus Notes and Comments Dynamic Bargaining Procedures for the Kernel and the Bargaining Set Dynamic Systems for the Kernel and the Bargaining Set Stable Sets of the Kernel and the Bargaining Set Asymptotic Stability of the Nucleolus Notes and Comments 199 Part II NTU Games 11 Cooperative Games in Strategic and Coalitional Form Cooperative Games in Strategic Form a- and ^-Effectiveness Coalitional Games with Nontransferable Utility 209

6 11.4 Cooperative Games with Side Payments but Without Transferable Utility Notes and Comments The Core of NTU Games Individual Rationality, Pareto Optimality, and the Core Balanced NTU Games Ordinal and Cardinal Convex Games Ordinal Convex Games Cardinal Convex Games An Axiomatization of the Core Reduced Games of NTU Games Axioms for the Core Proof of Theorem Additional Properties and Characterizations Notes and Comments The Shapley NTU Value and the Harsanyi Solution The Shapley Value of NTU Games A Characterization of the Shapley NTU Value The Harsanyi Solution A Characterization of the Harsanyi Solution Notes and Comments The Consistent Shapley Value For Hyperplane Games For p-smooth Games Axiomatizations The Role of IIA Logical Independence Notes and Comments 267 XI

7 XII 15 On the Classical Bargaining Set and the Mas-Colell Bargaining Set for NTU Games Preliminaries The Bargaining Set M The Mas-Colell Bargaining Set MB and Majority Voting Games The 3 x 3 Voting Paradox Voting Games with an Empty Mas-Colell Bargaining Set Non-levelled NTU Games with an Empty Mas-Colell Prebargaining Set The Example Non-levelled Games Existence Results for Many Voters Notes and Comments Variants of the Davis-Maschler Bargaining Set for NTU Games The Ordinal Bargaining Set M A Proof of Billera's Theorem Solutions Related to M The Ordinal Reactive and the Ordinal Semi-Reactive Bargaining Sets Solutions Related to the Prekernel ' Notes and Comments 308 References 311 Author Index 321 Subject Index 323