Introduction to the Theory of Cooperative Games (Theory and Decision Library C)

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9783540729440: Introduction to the Theory of Cooperative Games (Theory and Decision Library C)

This book systematically presents the main solutions of cooperative games: the core, bargaining set, kernel, nucleolus, and the Shapley value of TU games as well as the core, the Shapley value, and the ordinal bargaining set of NTU games. The authors devote a separate chapter to each solution, wherein they study its properties in full detail. In addition, important variants are defined or even intensively analyzed.

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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)

About the Author:

Bezalel Peleg is professor emeritus of mathematics and fellow of the Center for Rationality and Interactive Decision Theory of the Hebrew University of Jerusalem. He is a fellow of the Econometric Society and the author of Game Theoretic Analysis of Voting in Committees (1984). He published articles in various journals of mathematics, economic theory, social choice and welfare, game theory, and other fields. Peter Sudhölter is associate professor at the Department of Economics of the University of Southern Denmark at Odense. His list of publications indicates his interest in game theory with some emphasis on axiomatic approaches.

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