Models in cooperative game theory

Professor Dr. Rodica Branzei, PD Dr. Dinko Dimitrov, Professor Dr. Stef Tijs (auth.)3540779531, 9783540779537, 9783540779544

Cooperative game theory is a booming research area with many new developments in the last few years. So, our main purpose when prep- ing the second edition was to incorporate as much of these new dev- opments as possible without changing the structure of the book. First, this o?ered us the opportunity to enhance and expand the treatment of traditional cooperative games, called here crisp games, and, especially, that of multi-choice games, in the idea to make the three parts of the monograph more balanced. Second, we have used the opportunity of a secondeditiontoupdateandenlargethelistofreferencesregardingthe threemodels of cooperative games. Finally, we have bene?ted fromthis opportunity by removing typos and a few less important results from the ?rst edition of the book, and by slightly polishing the English style and the punctuation, for the sake of consistency along the monograph. The main changes are: (1) Chapter 3 contains an additional section, Section 3. 3, on the – erage lexicographic value, which is a recent one-point solution concept de?ned on the class of balanced crisp games. (2) Chapter 4 is new. It o?ers a brief overview on solution c- cepts for crisp games from the point of view of egalitarian criteria, and presents in Section 4. 2 a recent set-valued solution concept based on egalitarian considerations, namely the equal split-o? set. (3)Chapter5isbasicallyanenlargedversionofChapter4ofthe?rst edition because Section 5. 4 dealing with the relation between convex games and clan games with crisp coalitions is new.

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Table of contents :
Front Matter….Pages I-XI
Front Matter….Pages 1-3
Preliminaries….Pages 5-12
Cores and Related Solution Concepts….Pages 13-23
The Shapley Value, the τ -value, and the Average Lexicographic Value….Pages 25-35
Egalitarianism-based Solution Concepts….Pages 37-42
Classes of Cooperative Crisp Games….Pages 43-72
Front Matter….Pages 73-76
Preliminaries….Pages 77-81
Solution Concepts for Fuzzy Games….Pages 83-102
Convex Fuzzy Games….Pages 103-125
Fuzzy Clan Games….Pages 127-139
Front Matter….Pages 141-143
Preliminaries….Pages 145-148
Solution Concepts for Multi-Choice Games….Pages 149-164
Classes of Multi-Choice Games….Pages 165-192
Back Matter….Pages 193-203