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Introduction to the Theory of Cooperative Games

  • Bezalel Peleg
  • Peter Sudhölter

Part of the Theory and Decision Library book series (TDLC, volume 34)

About this book

Introduction

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)

Keywords

Axiomatic Analysis Cooperative Games Core NTU Games game theory

Authors and affiliations

  • Bezalel Peleg
    • 1
  • Peter Sudhölter
    • 2
  1. 1.Institute of Mathematics and Center for the Study of RationalityThe Hebrew University of JerusalemJerusalemIsrael
  2. 2.Department of Business and EconomicsUniversity of Southern DenmarkOdense MDenmark

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-72945-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2007
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Business and Economics
  • Print ISBN 978-3-540-72944-0
  • Online ISBN 978-3-540-72945-7
  • Series Print ISSN 0924-6126
  • Buy this book on publisher's site