Texts and Readings in Mathematics

This book is an introductory graduate-level text on game theory that grew out of courses in mathematics and economics and operations research.

Game theory deals with mathematical models of conflict and cooperation. In the first nine chapters, the author covers noncooperative games in extensive and strategic form and some economic applications. Relations with the theory of linear programing and the theory of linear complementarity are indicated.

The last chapter treats different types of cooperative games and solution concepts. Discussed are economic applications and applications in OR-situations with multiple agents.

The book includes a rich collection of exercises, partly with solutions.
1. Introduction
2. Game in Strategic form
3. Two-person zero-sum games
4. Mixed extensions of bimatrix games
5. The Nash equilibria of a 3-person game
6. Linear programming and matrix games
7. Linear complementarity and bimatrix games
8. Potential games
9. Other topics in non-cooperative game theory
10. Games in coalitional form
11. The imputation set and the core
12. Linear production games
13. Dominance, the D-core and stable sets
14. The Shapley value
15. The r-value
16. The nucleolus
17. Bargaining games
18. NTU-games
19. The NTU-value
A Solutions of Exercises
B Extra exercises
Bibliography
Index