Handbook of game theory. Vol. 4
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 lead to new ideas in game theory. Chapter 11 reviews game theory in biology, which is an excellent source for ideas, e.g., evolutionary game theory. Chapter 12 presents classical and recent developments in epistemic game theory. Chapter 13 provides an overview of the theory of population games and deterministic evolutionary dynamics. Chapter 14 develops the necessary background and formalism to understand the complexity of computing equilibria in some kind of games. Chapter 15 presents a systematic development of the theory of combinatorial games. Chapter 16 provides an overview of some developments of game theoretic methods as a framework of distributed control in engineered systems. Chapter 17 reviews developments of decision making under risk and uncertainty with departure from linearity in probabilities and sure thing principles. Chapter 18 surveys and discusses the recent literature on testing probabilistic forecasts ``strategic hypothesis testing''. A related reference to both Chapters 3 and 6 is [loc. cit.]. Publisher's description: The ability to understand and predict behavior in strategic situations, in which an individual's success in making choices depends on the choices of others, has been the domain of game theory since the 1950s. Developing the theories at the heart of game theory has resulted in 8 Nobel Prizes and insights that researchers in many fields continue to develop. In Volume 4, top scholars synthesize and analyze mainstream scholarship on games and economic behavior, providing an updated account of developments in game theory since the 2002 publication of Volume 3 [\textit{R. Aumann} (ed.) and \textit{S. Hart} (ed.) Handbook of game theory with economic applications. Vol. 3. Amsterdam: Elsevier (2002; Zbl 0993.90001)], which only covers work through the mid 1990s. {\parindent=5mm \begin{itemize}\item[{\(\bullet\)}] Focuses on innovation in games and economic behavior. \item[{\(\bullet\)}] Presents coherent summaries of subjects in game theory \item[{\(\bullet\)}] Makes details about game theory accessible to scholars in fields outside economics \end{itemize}} For Volumes 1 and 2 see [Zbl 0899.90166; Zbl 0993.90001].
scientific article; zbMATH DE number 6345345