Cooperative games, solutions and applications.

*(English)*Zbl 0686.90043The monograph presents the current state of knowledge in the area of cooperative games with finitely many players (in the characteristic function form) with special attention given to some topics of particular interest to the author and S. H. Tijs.

The first chapter includes definitions and several examples: a production economy, an exchange economy, the airport game, the bankruptcy game, the water resource development game and simple games. The second chapter reviews the solution concepts: Shapley value, stable sets, core, bargaining set, (pre)kernel, nucleolus and others. The fourth chapter presents results concerning the above concepts in the case of convex games.

The four remaining chapters deal with more specific problems: the Tijs’ \(\tau\)-value, game-theoretic concepts (\(\tau\)-value and nucleolus) in the cost allocation problems, division rules and bankruptcy problems (application of the Shapley value, nucleolus and \(\tau\)-value) and, finally, the author’s own theory of k-convex games.

The first chapter includes definitions and several examples: a production economy, an exchange economy, the airport game, the bankruptcy game, the water resource development game and simple games. The second chapter reviews the solution concepts: Shapley value, stable sets, core, bargaining set, (pre)kernel, nucleolus and others. The fourth chapter presents results concerning the above concepts in the case of convex games.

The four remaining chapters deal with more specific problems: the Tijs’ \(\tau\)-value, game-theoretic concepts (\(\tau\)-value and nucleolus) in the cost allocation problems, division rules and bankruptcy problems (application of the Shapley value, nucleolus and \(\tau\)-value) and, finally, the author’s own theory of k-convex games.

Reviewer: A.Wieczorek

##### MSC:

91A12 | Cooperative games |

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

91A40 | Other game-theoretic models |

91B38 | Production theory, theory of the firm |

91B50 | General equilibrium theory |

91B60 | Trade models |

91B24 | Microeconomic theory (price theory and economic markets) |