Game theory: analysis of conflict.

*(English)*Zbl 0729.90092
Cambridge, MA: Harvard University Press. xiii, 568 p. $ 45.95/hbk (1991).

The book under review is a textbook on game theory, with the main bulk and additional material clearly separated and exercises added for educational purposes. It comprises all the basic ideas and methods of game theory, but with specific and not-so-common emphasis on the author’s own field of expertise: non-cooperative games and games with non- transferable utility (NTU). The book is written with applications in mind, and such games are really important, because in many real-life applications of game theory communications and transfer of utility between the players are essentially limited.

Chapter 1 is devoted to the foundations of utility theory. It describes the usual rationality axioms, how they lead to utility and why real-life behavior is sometimes not rational in this sense. Chapter 2 describes general models with moves, complete or incomplete information, again with a thorough discussion of to what extent these models describe real-life conflicts. Chapters 3 to 5 describe games in the strategic form: Chapter 3 introduces main definitions and the classical results for zero-sum games, Chapter 4 and 5 describe how to compute equilibria and related strategies efficiently for various equilibrium criteria. In Chapter 6 similar games are studied, in which the possibility of partial cooperation is added. In Chapter 7 specific features of repetitive games are analyzed. In Chapter 8-10 games with unrestricted cooperation are analyzed. The exposition includes both the transferable utility case that is well represented in standard textbooks, and the more realistic NTU (non-transferable utility) case (that gives, in particular, a transparent exposition of the author’s research). Chapter 8 describes Nash’s bargaining scheme, its axiomatic derivation and similar schemes; Chapter 9 describes coalitions, core, Shapley value and their generalizations to a NTU case. In Chapter 10 all these notions are further generalized to the case, when in order to make the model even more realistic we add the real-life fact that even if all the strategies are fixed, the outcome can be only predicted with some uncertainty. This case is illustrated by realistic bargaining examples.

Chapter 1 is devoted to the foundations of utility theory. It describes the usual rationality axioms, how they lead to utility and why real-life behavior is sometimes not rational in this sense. Chapter 2 describes general models with moves, complete or incomplete information, again with a thorough discussion of to what extent these models describe real-life conflicts. Chapters 3 to 5 describe games in the strategic form: Chapter 3 introduces main definitions and the classical results for zero-sum games, Chapter 4 and 5 describe how to compute equilibria and related strategies efficiently for various equilibrium criteria. In Chapter 6 similar games are studied, in which the possibility of partial cooperation is added. In Chapter 7 specific features of repetitive games are analyzed. In Chapter 8-10 games with unrestricted cooperation are analyzed. The exposition includes both the transferable utility case that is well represented in standard textbooks, and the more realistic NTU (non-transferable utility) case (that gives, in particular, a transparent exposition of the author’s research). Chapter 8 describes Nash’s bargaining scheme, its axiomatic derivation and similar schemes; Chapter 9 describes coalitions, core, Shapley value and their generalizations to a NTU case. In Chapter 10 all these notions are further generalized to the case, when in order to make the model even more realistic we add the real-life fact that even if all the strategies are fixed, the outcome can be only predicted with some uncertainty. This case is illustrated by realistic bargaining examples.

Reviewer: O.M.Kosheleva (El Paso)

##### MSC:

91A05 | 2-person games |

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

91A10 | Noncooperative games |

91A20 | Multistage and repeated games |

91B16 | Utility theory |

91A12 | Cooperative games |

91A80 | Applications of game theory |