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Economics - Game Theory / Mathematical Methods | Introduction to the Theory of Cooperative Games

Introduction to the Theory of Cooperative Games

Peleg, Bezalel, Sudhölter, Peter

Originally published by Springer US, 2003

2nd ed. 2007, XIX, 328 p.

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  • Offers a detailed analysis and unified axiomatic treatment of the main solutions of cooperative games, both with and without side payments
  • Suitable for introductory and graduate courses on game theory

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)

Content Level » Research

Keywords » Axiomatic Analysis - Cooperative Games - Core - NTU Games - game theory

Related subjects » Applications - Economic Theory - Game Theory / Mathematical Methods

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