Models in Cooperative Game Theory

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.

Cooperative Games with Crisp Coalitions. - Preliminaries. - Cores and Related Solution Concepts. - The Shapley Value, the ? -value, and the Average Lexicographic Value. - Egalitarianism-based Solution Concepts. - Classes of Cooperative Crisp Games. - Cooperative Games with Fuzzy Coalitions. - Preliminaries. - Solution Concepts for Fuzzy Games. - Convex Fuzzy Games. - Fuzzy Clan Games. - Multi-Choice Games. - Preliminaries. - Solution Concepts for Multi-Choice Games. - Classes of Multi-Choice Games.