Handbook of game theory. Vol. 4
type: Item
instance of: scholarly article
title: Handbook of game theory. Vol. 4
zbMATH Open document ID: 1304.91001
published in: Handbooks in Economics
publication date: 2014-09-17T00:00:00Z
full work available at URL: http://www.sciencedirect.com/science/handbooks/15740005
review text: The ability to make decisions in situations where one's payoff depends on others' decisions is the domain of game theory. Since human behavior is more complicated than models, game theory has to be updated continuously. This book is an updated account of developments in game theory. Chapter 1 discusses rationality, its different definitions and different motivations. The concept of small world here differs from the concept of small world networks. Chapter 2 gives a review of new results on two-person zero-sum games. Some relations with differential, stochastic and continuous-time games are given. The reviewer wants to point out that the behavior of a dynamical system and its discretization typically differs in their stability, bifurcation and chaotic conditions. They agree only in their fixed point (equilibrium). Networks can significantly change the outcome of games [\textit{G. Szabó} and \textit{G. Fáth}, ``Evolutionary games on graphs'', Phys. Rep. 446, 97--216 (2007; \url{doi:10.1016/j.physrep.2007.04.004})]. Chapter 3 concerns social games on networks and the effect of the structure of the network on the game outcome. Chapter 4 surveys results on reputations in repeated games of incomplete information. Chapter 5 surveys results on coalition formation. Chapter 6 studies stochastic evolutionary game dynamics. Evolutionary games differ from traditional games in two aspects: a large population and the use of simple adaptive rules. Moreover, stochasticity is a known realistic factor which, in some cases, has significant effects. Therefore, the reviewer believes that this topic is quite important. Chapters 7--9 survey different aspects of auctions. An update of developments and applications is given in Chapter 7. Combinatorial auctions are studied in Chapter 8. Algorithmic mechanism design applied to multiunit auctions is studied in Chapter 9. Chapter 10 reviews recent experimental data testing game theory. This is important since, if discrepancies exist, such tests …
Mathematics Subject Classification ID: 91-00
Mathematics Subject Classification ID: 91-06
Mathematics Subject Classification ID: 91Axx
Mathematics Subject Classification ID: 91A80
Mathematics Subject Classification ID: 91Bxx
Mathematics Subject Classification ID: 00B15
zbMATH DE Number: 6345345
zbMATH Keywords: game theory
zbMATH Keywords: applications in economics
zbMATH Keywords: applications in biology
reviewed by: Ahmed Hegazi
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6345345