A Course on Cooperative Game Theory

This book deals with situations where objectives of participants of the game are partially cooperative and partially conflicting.

Satya R. Chakravarty (Author), Manipushpak Mitra (Author), Palash Sarkar (Author)

9781107691322, Cambridge University Press

Paperback / softback, published 17 October 2014

276 pages
22.9 x 15.3 x 1.3 cm, 0.36 kg

Cooperative game theory deals with situations where objectives of participants of the game are partially cooperative and partially conflicting. It is in the interest of participants to cooperate in the sense of making binding agreements to achieve the maximum possible benefit. When it comes to distribution of benefit/payoffs, participants have conflicting interests. Such situations are usually modelled as cooperative games. While the book mainly discusses transferable utility games, there is also a brief analysis of non-transferable utility games. Alternative solution concepts to cooperative game theoretic problems are presented in chapters 1-9 and the next four chapters present issues related to computations of solutions discussed in the earlier chapters. The proofs of all results presented in the book are quite explicit. Additionally the mathematical techniques employed in demonstrating the results will be helpful to those who wish to learn application of mathematics for solving problems in game theory.

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.

Subject Areas: Game theory [PBUD], Optimization [PBU], Microeconomics [KCC], Economics [KC]