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**Dynamic noncooperative game theory.**
*(English)*
Zbl 0828.90142

London: Academic Press. xii, 519 p. (1995).

This is the second enlarged edition of a previous book of the authors with identical title (1982; Zbl 0479.90085). It presents an extensive and updated treatment of static and dynamic noncooperative game theory: static games in normal and extensive form (about 20%), dynamic games (30%), finite games (20%), and infinite games (30%). Two- and \(N\)- person both zero-sum and non-zero-sum games are studied. Two main concepts of equilibrium are studied, namely: saddle point and Nash equilibrium (about 70%) and the Stackelberg solution (about 30% of the volume).

New material consists of: randomized strategies, finite games with repeated decisions and action-dependent information sets, various refinements of the Nash equilibrium concept, stability of Nash equilibria and its relation with numerical schemes, some new theorems on the existence of Nash equilibria (in the first part), time consistency, viscosity solutions of the Hamilton-Jacobi-Bellman equation, affine- quadratic dynamic games, infinite-horizon games, incentive theory and relationship with Stackelberg solution, Stackelberg equilibrium in the continuous time (in the second part).

Some specific types of zero-sum games on the square and the material on the dolichobrachistochrone from the first edition have been cancelled.

New material consists of: randomized strategies, finite games with repeated decisions and action-dependent information sets, various refinements of the Nash equilibrium concept, stability of Nash equilibria and its relation with numerical schemes, some new theorems on the existence of Nash equilibria (in the first part), time consistency, viscosity solutions of the Hamilton-Jacobi-Bellman equation, affine- quadratic dynamic games, infinite-horizon games, incentive theory and relationship with Stackelberg solution, Stackelberg equilibrium in the continuous time (in the second part).

Some specific types of zero-sum games on the square and the material on the dolichobrachistochrone from the first edition have been cancelled.

Reviewer: Z.Wyderka (Katowice)

### MSC:

91A10 | Noncooperative games |

91-02 | Research exposition (monographs, survey articles) pertaining to game theory, economics, and finance |

49L25 | Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games |

91A50 | Discrete-time games |

91A65 | Hierarchical games (including Stackelberg games) |