Книга(Modeles in cooperative games)

Книга(Modeles in cooperative games)

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Rodica Branzei, Dinko Dimitrov, Stef Tijs Models in Cooperative Game Theory: Crisp, Fuzzy and Multichoice Games – Monograph – January 14, 2005 Springer Berlin Heidelberg NewYork Hong Kong London Milan Paris Tokyo Preface This book investigates the classical model of cooperative games with trans- ferable utility (TU-games) and models in which the players have the possi- bility to cooperate partially, namely fuzzy and multichoice games. In a crisp game the agents are either fully involved or not involved at all in coopera- tion with some other agents, while in a fuzzy game players are allowed to cooperate with infinitely many different participation levels, varying from non-cooperation to full cooperation. A multichoice game describes an in- termediate case in which each player may have a fixed number of activity levels. Part I of the book is devoted to the most developed model in the theory of cooperative games, that of a classical TU-game with crisp coalitions, which we refer to as crisp game along the book. It presents basic notions, solutions concepts and classes of cooperative crisp games in such a way that allows the reader to use this part as a reference toolbox when studying the corresponding concepts from the theory of fuzzy games (Part II) and from the theory of multichoice games (Part III). The work on this book started while we were research fellows at ZiF (Bielefeld) for the project “Procedural Approaches to Conflict Resolution”, 2002. We thank our hosts Matthias Raith and Olaf Gaus for giving us the possibility to freely structure our research plans as well as the officials from the ZiF administration for their kind hospitality. The work of Dinko Dimitrov was generously supported by a Marie Curie Research Fellowship of the European Community programme “Improving the Human Research Potential and the Socio-Economic Knowledge Base” under contract number HPMF-CT-2002-02121 conducted at Tilburg. Thanks are also due to Luis VI Preface G. Gonz´ alez Morales for transforming the manuscript into this final version. Tilburg, Rodica Branzei January 2005 Dinko Dimitrov Stef Tijs Contents Part I Cooperative games with crisp coalitions 1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Cores and related solution concepts . . . . . . . . . . . . . . . . . . . . . 13 2.1 Imputations, cores and stable sets . . . . . . . . . . . . . . . . . . . . . . 13 2.2 The core cover, the reasonable set and the Weber set . . . . . 18 3 The Shapley value and the τ-value . . . . . . . . . . . . . . . . . . . . . . 23 3.1 The Shapley value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2 The τ-value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4 Classes of cooperative crisp games . . . . . . . . . . . . . . . . . . . . . . 31 4.1 Totally balanced games . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.1.1 Basic characterizations . . . . . . . . . . . . . . . . . . . . . . . . . .Basic characterizations ....
View Full Document

Page1 / 142

Книга(Modeles in cooperative games)

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online