Understanding game theory. Introduction to the analysis of many agent systems with competition and cooperation. (English) Zbl 1189.91001

Kolokoltsov, Vassili N.; Malafeyev, Oleg A.

Hackensack, NJ: World Scientific (ISBN 978-981-4291-71-2/hbk). xiv, 286 p. (2010).

This book is devoted to game theory and its applications. It consists of two parts. The first part contains the main ideas of game theory. In numerous examples the authors clarify the essence and nature of conflict. Here the models related with the prisoner’s dilemma, auctions, voting procedures and cooperation theory are presented. Most of the examples have some interesting illustrations from classical literature, music and political economies. In the second part the mathematical methods are described. This part is devoted to some selected topics of more advanced analysis including the differential geometry approach to stability, the dynamic system approach to the analysis of differential games, Bellman type equations for multi-criteria optimization, turnpikes for stochastic games and connections with idempotent mathematics. The material from the first part can serve as a basis for an introductory undergraduate course in game theory for both mathematics related degrees and university degrees in economics, business, etc. The second part is meant mostly for mathematics graduate and postgraduate students.

Reviewer: Vladimir Mazalov (Petrozavodsk)

MSC:

91-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to game theory, economics, and finance
91Axx	Game theory

Keywords:

game theory; textbook; prisoner’s dilemma; auctions; voting procedures; cooperation; differential geometry approach to stability; dynamic system approach; differential games; Bellman equations; turnpikes for stochastic games