Models in Cooperative Game Theory (eBook)

Rodica Branzei, Dinko Dimitrov, Stef Tijs (Autoren)

eBook Download: PDF

2008 | 2nd ed. 2008
XII, 204 Seiten
Springer Berlin (Verlag)
978-3-540-77954-4 (ISBN)

Infos

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.

Inhalt

Preface 5
Preface to the First Edition 7
Contents 9
Part I Cooperative Games with Crisp Coalitions 13
1 Preliminaries 16
2 Cores and Related Solution Concepts 24
2.1 Imputations, Cores and Stable Sets 24
2.2 The Core Cover, the Reasonable Set and the Weber Set 31
3The Shapley Value, the t -value, and theAverage Lexicographic Value 36
3.1 The Shapley Value 36
3.2 The t -value 42
3.3 The Average Lexicographic Value 44
4 Egalitarianism-based Solution Concepts 48
4.1 Overview 48
4.2 The Equal Split-O. Set 49
5 Classes of Cooperative Crisp Games 54
5.1 Totally Balanced Games 54
5.2 Convex Games 57
5.3 Clan Games 70
5.4 Convex Games versus Clan Games 76
Part II Cooperative Games with Fuzzy Coalitions 84
6 Preliminaries 88
7 Solution Concepts for Fuzzy Games 94
7.1 Imputations and the Aubin Core 94
7.2 Cores and Stable Sets 96
7.3 Generalized Cores and Stable Sets 100
7.4 The Shapley Value and the Weber Set 105
7.5 Path Solutions and the Path Solution Cover 107
7.6 Compromise Values 111
8 Convex Fuzzy Games 114
8.1 Basic Characterizations 114
8.2 Egalitarianism in Convex Fuzzy Games 121
8.3 Participation Monotonic Allocation Schemes 127
8.4 Properties of Solution Concepts 130
9 Fuzzy Clan Games 138
9.1 The Cone of Fuzzy Clan Games 138
9.2 Cores and Stable Sets for Fuzzy Clan Games 142
9.3 Bi-Monotonic Participation Allocation Rules 146
Part III Multi-Choice Games 152
10 Preliminaries 156
11 Solution Concepts for Multi-Choice Games 160
11.1 Imputations, Cores and Stable Sets 160
11.2 Marginal Vectors and the Weber Set 166
11.3 Shapley-like Values 170
11.4 The Equal Split-O. Set for Multi-Choice Games 174
12 Classes of Multi-Choice Games 176
12.1 Balanced Multi-Choice Games 176
12.2 Convex Multi-Choice Games 181
12.3 Multi-Choice Clan Games 193
References 204
Index 212

Produkt-Details

• Erscheint lt. Verlag: 8.3.2008
• Zusatzinfo: XII, 204 p.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Technik
• Themenwelt: Wirtschaft ► Allgemeines / Lexika
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management ► Planung / Organisation
• Themenwelt: Wirtschaft ► Volkswirtschaftslehre
• Schlagworte: Addition • Agents • average • Cooperation • Cooperative games • cooperative game theory • Finite • fuzzy • Fuzzy games • Games • Game Theory • Layers • Multi-choice Games • SET
• ISBN-10: 3-540-77954-X / 354077954X
• ISBN-13: 978-3-540-77954-4 / 9783540779544