Games and dynamic games
type: Item
instance of: scholarly article
zbMATH Open document ID: 1396.91003
author: Jacek B. Krawczyk
author: Alain Haurie
author: Georges Zaccour
publication date: 2014-10-13T00:00:00Z
Mathematics Subject Classification ID: 91-01
Mathematics Subject Classification ID: 91A25
Mathematics Subject Classification ID: 91A10
Mathematics Subject Classification ID: 91A15
Mathematics Subject Classification ID: 91A23
Mathematics Subject Classification ID: 91A50
Mathematics Subject Classification ID: 00A06
zbMATH DE Number: 6354775
zbMATH Keywords: dynamic games
zbMATH Keywords: static games
zbMATH Keywords: stochastic games
zbMATH Keywords: dynamic programming
zbMATH Keywords: maximum principle
MaRDI profile type: Publication
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title: Games and dynamic games
published in: World Scientific--Now Publishers Series in Business
review text: This book addresses a comprehensive study of the theory of static and dynamic games. It contains the most studied models appearing in the literature and at the same time provides interesting applications. The book is well written and is mainly addressed to graduate students of engineering, management science and operations research.NEWLINENEWLINEAfter an introductory chapter, the contents of the book can be divided into three parts; namely, static games, deterministic dynamic games and stochastic dynamic games.NEWLINENEWLINEThe first part regards to the classical theory of games in the static case. This part is divided into three chapters. NEWLINENEWLINENEWLINEChapter 2 (``Description of the game'') provides a complete description of the elements of a game, such as the concepts of players, actions, strategies, information structure, payoffs, among others. Furthermore, the two different representations of a game are introduced; namely, the extensive form (represented by a graph) and the normal form (posed in terms of the payoff and the strategies of the players). Some empirical methods to deduce ``optimality'' for the players in a game are discussed as well.NEWLINENEWLINE In Chapter 3 (``Equilibrium solutions for noncooperative games''), the aim of the authors is to obtain noncooperative equilibria in different types of games. To this end, the concept of Nash equilibrium is introduced first, and then two different types of games are introduced: the so-called matrix and bimatrix games. The analysis of these games, does not only focus on the existence of saddle points (for matrix games) or Nash equilibria (for bimatrix games), but also useful algorithms are deeply analyzed to obtain these classes of equilibria. Some shortcomings of the Nash equilibrium concept are also discussed; in particular, its inefficiency as reflected in the prisoner's dilemma. Finally, the last part of this chapter studies the concept of the Stackelberg equilibrium, showing the existence of this…
description: scientific article; zbMATH DE number 6354775