Preface	6
	Contents	10
	List of Figures	12
	to 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
	to 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
	to 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
	to 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
	to 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 ?-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
	to 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