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Game theory. A multi-leveled approach. (English) Zbl 1147.91001

Berlin: Springer (ISBN 978-3-540-69290-4/hbk; 978-3-642-42625-4/pbk; 978-3-540-69291-1/ebook). xv, 365 p. (2008).
The book consists of an introductory chapter followed by three major sections, or “Parts”. In the introduction, zero-sum games, nonzero-sum games, extensive form games, cooperative games and bargaining games are introduced by examples, and the ideas of strategy, mixed strategy, saddle point, Nash equilibrium, illustrated. Part I, Chapters 2-11, is intended for undergraduates in economics and business, and as background for Parts II-IV. A basic undergraduate course for such students (or for mathematics students) could be built on Chapters 2-6 and 9, which cover finite two-person games, finite extensive form games, finite games with incomplete information, further extensions of ideas in noncooperative games, and cooperative games with transferable utility. Parts II-IV require more mathematical sophistication, and are aimed at graduate students in economics, or could be used for an elective course in game theory by students in applied mathematics. Part II, Chapters 12-15, is on noncooperative games. Part III, chapters16-21, on cooperative games, covers core, Shapley value, Weber set, nucleolus, and much more. Part IV, Tools, consisting of Chapter 22 only, collects some of the mathematical tools used in the book, such as convex separation, Farkas’ Lemma, linear duality theorem, fixed point theorems, Krein-Milman Theorem, and more. Each chapter closes with a set of problems, with hints, answers and solutions at the back of the book.

MSC:

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