Ebook: Introduction to the Theory of Cooperative Games
- Tags: Game Theory/Mathematical Methods, Economic Theory, Game Theory Economics Social and Behav. Sciences
- Series: Theory and Decision Library 34
- Year: 2007
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 2
- Language: English
- pdf
This book systematically presents the main solutions of cooperative games: the core, bargaining set, kernel, nucleolus, and the Shapley value of TU games, and the core, the Shapley value, and the ordinal bargaining set of NTU games. To each solution the authors devote a separate chapter wherein they study its properties in full detail. Moreover, important variants are defined or even intensively analyzed. The authors also investigate in separate chapters continuity, dynamics, and geometric properties of solutions of TU games. The study culminates in uniform and coherent axiomatizations of all the foregoing solutions (excluding the bargaining set). Such axiomatizations have not appeared in any book. Moreover, the book contains a detailed analysis of the main results on cooperative games without side payments. Such analysis is very limited or non-existent in other books on game theory.
"Bezalel Peleg and Peter Sudhölter's book is a welcome addition to any game theory library. The book provides comprehensive coverage of the theory of cooperative games and, as such, would make useful reference book for researchers interested cooperative games. One of the strengths of this book is its treatment of non-transferable utility (NTU) games... Another strength is the emphasis the early chapters of the book on the link to mathematical programming. The book is readable but rigorous and this should contribute to its success." R. Beard, Economic Record (2004)
"The text provides a thorough, detailed, rigorous, precise and complete account of the axiomatic treatment of solution concepts of cooperative games. ... concrete mathematical examples and counterexamples, along with existence and nonexistence results concerning a variety of solution concepts, are offered. ... an excellent, comprehensive, and clearly presented source of information about the mathematics of cooperative games." Zvi Artstein, SIAM Review (2005)
"This book contains a lot of material that would be hard to dig up in the literature. It certainly should be on the shelf of any researcher of game theory." M. Maschler, Games and Economic Behavior (2005)
This book systematically presents the main solutions of cooperative games: the core, bargaining set, kernel, nucleolus, and the Shapley value of TU games, and the core, the Shapley value, and the ordinal bargaining set of NTU games. To each solution the authors devote a separate chapter wherein they study its properties in full detail. Moreover, important variants are defined or even intensively analyzed. The authors also investigate in separate chapters continuity, dynamics, and geometric properties of solutions of TU games. The study culminates in uniform and coherent axiomatizations of all the foregoing solutions (excluding the bargaining set). Such axiomatizations have not appeared in any book. Moreover, the book contains a detailed analysis of the main results on cooperative games without side payments. Such analysis is very limited or non-existent in other books on game theory.
"Bezalel Peleg and Peter Sudh?lter's book is a welcome addition to any game theory library. The book provides comprehensive coverage of the theory of cooperative games and, as such, would make useful reference book for researchers interested cooperative games. One of the strengths of this book is its treatment of non-transferable utility (NTU) games... Another strength is the emphasis the early chapters of the book on the link to mathematical programming. The book is readable but rigorous and this should contribute to its success." R. Beard, Economic Record (2004)
"The text provides a thorough, detailed, rigorous, precise and complete account of the axiomatic treatment of solution concepts of cooperative games. ... concrete mathematical examples and counterexamples, along with existence and nonexistence results concerning a variety of solution concepts, are offered. ... an excellent, comprehensive, and clearly presented source of information about the mathematics of cooperative games." Zvi Artstein, SIAM Review (2005)
"This book contains a lot of material that would be hard to dig up in the literature. It certainly should be on the shelf of any researcher of game theory." M. Maschler, Games and Economic Behavior (2005)
This book systematically presents the main solutions of cooperative games: the core, bargaining set, kernel, nucleolus, and the Shapley value of TU games, and the core, the Shapley value, and the ordinal bargaining set of NTU games. To each solution the authors devote a separate chapter wherein they study its properties in full detail. Moreover, important variants are defined or even intensively analyzed. The authors also investigate in separate chapters continuity, dynamics, and geometric properties of solutions of TU games. The study culminates in uniform and coherent axiomatizations of all the foregoing solutions (excluding the bargaining set). Such axiomatizations have not appeared in any book. Moreover, the book contains a detailed analysis of the main results on cooperative games without side payments. Such analysis is very limited or non-existent in other books on game theory.
"Bezalel Peleg and Peter Sudh?lter's book is a welcome addition to any game theory library. The book provides comprehensive coverage of the theory of cooperative games and, as such, would make useful reference book for researchers interested cooperative games. One of the strengths of this book is its treatment of non-transferable utility (NTU) games... Another strength is the emphasis the early chapters of the book on the link to mathematical programming. The book is readable but rigorous and this should contribute to its success." R. Beard, Economic Record (2004)
"The text provides a thorough, detailed, rigorous, precise and complete account of the axiomatic treatment of solution concepts of cooperative games. ... concrete mathematical examples and counterexamples, along with existence and nonexistence results concerning a variety of solution concepts, are offered. ... an excellent, comprehensive, and clearly presented source of information about the mathematics of cooperative games." Zvi Artstein, SIAM Review (2005)
"This book contains a lot of material that would be hard to dig up in the literature. It certainly should be on the shelf of any researcher of game theory." M. Maschler, Games and Economic Behavior (2005)
Content:
Front Matter....Pages I-XIX
Introduction....Pages 1-6
Front Matter....Pages 7-7
Coalitional TU Games and Solutions....Pages 9-26
The Core....Pages 27-49
Bargaining Sets....Pages 51-80
The Prekernel, Kernel, and Nucleolus....Pages 81-106
The Prenucleolus....Pages 107-132
Geometric Properties of the ?-Core, Kernel, and Prekernel....Pages 133-149
The Shapley Value....Pages 151-179
Continuity Properties of Solutions....Pages 181-188
Dynamic Bargaining Procedures for the Kernel and the Bargaining Set....Pages 189-199
Front Matter....Pages 201-201
Cooperative Games in Strategic and Coalitional Form....Pages 203-212
The Core of NTU Games....Pages 213-234
The Shapley NTU Value and the Harsanyi Solution....Pages 235-251
The Consistent Shapley Value....Pages 253-267
On the Classical Bargaining Set and the Mas-Colell Bargaining Set for NTU Games....Pages 269-293
Variants of the Davis-Maschler Bargaining Set for NTU Games....Pages 295-309
Back Matter....Pages 311-328
This book systematically presents the main solutions of cooperative games: the core, bargaining set, kernel, nucleolus, and the Shapley value of TU games, and the core, the Shapley value, and the ordinal bargaining set of NTU games. To each solution the authors devote a separate chapter wherein they study its properties in full detail. Moreover, important variants are defined or even intensively analyzed. The authors also investigate in separate chapters continuity, dynamics, and geometric properties of solutions of TU games. The study culminates in uniform and coherent axiomatizations of all the foregoing solutions (excluding the bargaining set). Such axiomatizations have not appeared in any book. Moreover, the book contains a detailed analysis of the main results on cooperative games without side payments. Such analysis is very limited or non-existent in other books on game theory.
"Bezalel Peleg and Peter Sudh?lter's book is a welcome addition to any game theory library. The book provides comprehensive coverage of the theory of cooperative games and, as such, would make useful reference book for researchers interested cooperative games. One of the strengths of this book is its treatment of non-transferable utility (NTU) games... Another strength is the emphasis the early chapters of the book on the link to mathematical programming. The book is readable but rigorous and this should contribute to its success." R. Beard, Economic Record (2004)
"The text provides a thorough, detailed, rigorous, precise and complete account of the axiomatic treatment of solution concepts of cooperative games. ... concrete mathematical examples and counterexamples, along with existence and nonexistence results concerning a variety of solution concepts, are offered. ... an excellent, comprehensive, and clearly presented source of information about the mathematics of cooperative games." Zvi Artstein, SIAM Review (2005)
"This book contains a lot of material that would be hard to dig up in the literature. It certainly should be on the shelf of any researcher of game theory." M. Maschler, Games and Economic Behavior (2005)
Content:
Front Matter....Pages I-XIX
Introduction....Pages 1-6
Front Matter....Pages 7-7
Coalitional TU Games and Solutions....Pages 9-26
The Core....Pages 27-49
Bargaining Sets....Pages 51-80
The Prekernel, Kernel, and Nucleolus....Pages 81-106
The Prenucleolus....Pages 107-132
Geometric Properties of the ?-Core, Kernel, and Prekernel....Pages 133-149
The Shapley Value....Pages 151-179
Continuity Properties of Solutions....Pages 181-188
Dynamic Bargaining Procedures for the Kernel and the Bargaining Set....Pages 189-199
Front Matter....Pages 201-201
Cooperative Games in Strategic and Coalitional Form....Pages 203-212
The Core of NTU Games....Pages 213-234
The Shapley NTU Value and the Harsanyi Solution....Pages 235-251
The Consistent Shapley Value....Pages 253-267
On the Classical Bargaining Set and the Mas-Colell Bargaining Set for NTU Games....Pages 269-293
Variants of the Davis-Maschler Bargaining Set for NTU Games....Pages 295-309
Back Matter....Pages 311-328
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