A Course on Cooperative Game Theory by Satya R. Chakravarty

Preface 1. Introduction and motivation page 2. Basics and preliminaries 3. The core and some related solutions 4. The bargaining set, kernel and nucleolus 5. The Shapley value 6. The core, Shapley value and Weber set 7. Voting games 8. Mathematical matching 9. Non-transferable utility cooperative games 10. Linear programming 11. Algorithmic aspects of cooperative game theory 12. Weighted majority games 13. Stable matching algorithm References Index

Cooperative game theory deals with those situations where objectives of the participants of a game are partially cooperative and partially conflicting. While the book mainly discusses transferable utility games, there is a brief analysis of non-transferable utility games. Chapters 1 to 9 focus on alternative solution concepts to cooperative game theoretic problems, followed by the issues related to computation of solutions in the next four chapters. The mathematical techniques employed in demonstrating the results will be helpful for solving problems in game theory. The authors have explained the concepts and results using extensive verbal reasoning. Integration of theory and practice helps the readers understand the theoretical issues first and then see their practical relevance. This book is a good starting point for researchers in cooperative games. Key features ? Discusses the recent developments in the area of cooperative game theory ? Presents an up-to-date systematic treatment of the concepts including core, stable set, bargaining set, kernel, nucleolus, the Shapley value and the Weber set ? Includes topics like voting games, mathematical matching, bargaining problems and computational algorithms of alternative solution concepts ? Provides intuitive explanations and illustrations of mathematical results