Introduction to the theory of games. Concepts, methods, applications
type: Item
instance of: scholarly article
title: Introduction to the theory of games. Concepts, methods, applications
zbMATH Open document ID: 0941.91001
author: Ferenc Forgó
author: J. Szép
author: F. Szidarovszky
published in: Nonconvex Optimization and Its Applications
publication date: 1999-10-10T00:00:00Z
review text: The book is a revised and expanded version of the edition, published in 1985 (Budapest: Akademici Kiado, see the review in Zbl 0578.90096). It intends not only to give concepts and models of modern game theory but also to survey methods for seeking game solutions. Nonconvex problems are discuss as well. The book covers almost all classical results of game theory except of differential, hierarchial, and position games. Some special classes of games, such as stochastic and combinatorial are not covered. However, other special classes, such as duels and Harsanyi models, are considered. The graduate course text features of the book are enhanced by the addition of problems and exercises. The book consists of two parts. Part I is devoted to noncooperative games. It has 13 chapters. Chapter 1 is introductory and defines extensive and normal forms of a game and a game tree. Next three chapters are devoted to Nash equilibrium (definition, existence, and uniqueness). The authors do not bound themselves by convex case but investigate various generalizations of concavity, in particular, concavity of the sum of the pay-off functions. Classical mixed extensions of finite games are introduced in Chapter 5 where proper and perfect equilibria are also discussed. Computation of mixed equilibria is considered in Chapter 6. Well-known methods are briefly mentioned, but Scarf-Hansen algorithm is only covered in details. Special attention is given to oligopoly games (Chapter 7): multi- and single-product cases. For dynamic oligopolies Cournot procedure is described (without Cournot name). For linear statements, its convergence is proved to be equivalent to duopoly case. Two-person games are thoroughly considered in Chapters 8 - 11 in a classical way. In Chapters 12 and 13 non-classical branches of game theory are presented: repeated games and games with incomplete information in the sence of Harsanyi approach. Part II is devoted to cooperative games. It has 10 chapters (14 - 23). Chapter…
Mathematics Subject Classification ID: 91Axx
Mathematics Subject Classification ID: 91-01
Mathematics Subject Classification ID: 91A05
Mathematics Subject Classification ID: 91A06
Mathematics Subject Classification ID: 91A10
Mathematics Subject Classification ID: 91A12
Mathematics Subject Classification ID: 91A20
Mathematics Subject Classification ID: 91A80
zbMATH DE Number: 1349349
zbMATH Keywords: game theory
zbMATH Keywords: equilibrium
zbMATH Keywords: oligopoly
zbMATH Keywords: cooperative games
zbMATH Keywords: incomplete information
zbMATH Keywords: bargaining
zbMATH Keywords: graduate students
reviewed by: N. M. Novikova
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1349349