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This book investigates the classical model of cooperative games with transfer able utility (TU-games) and models in which the players have the possibility to cooperate partially, namely fuzzy and multichoice games. In a crisp game the agents are either fully involved or not involved at all in cooperation 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 intermediate 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 (Biele feld) for the project "Procedural Approaches to Conflict Resolution", 2002.
Game theory. --- Mathematical models. --- Games, Theory of --- Theory of games --- Mathematical models --- Mathematics --- Models, Mathematical --- Simulation methods --- Economic theory. --- Mathematics. --- Operations research. --- Microeconomics. --- Economic Theory/Quantitative Economics/Mathematical Methods. --- Game Theory, Economics, Social and Behav. Sciences. --- Operations Research/Decision Theory. --- Math --- Science --- Price theory --- Economics --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Economic theory --- Political economy --- Social sciences --- Economic man --- Decision making. --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Decision making
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Cooperative game theory is a booming research area with many new developments in the last few years. So, our main purpose when preparing the second edition was to incorporate as much of these new developments as possible without changing the structure of the book. First, this offered 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 second edition to update and enlarge the list of references regarding the three models of cooperative games. Finally, we have benefited from this opportunity by removing typos and a few less important results from the first 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 average lexicographic value, which is a recent one-point solution concept defined on the class of balanced crisp games. (2) Chapter 4 is new. It offers a brief overview on solution concepts 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)Chapter 5 is basically an enlarged version of Chapter 4 of the first edition because Section 5. 4 dealing with the relation between convex games and clan games with crisp coalitions is new.
Fuzzy sets. --- Game theory. --- Games, Theory of --- Theory of games --- Mathematical models --- Mathematics --- Sets, Fuzzy --- Fuzzy mathematics --- Set theory --- Economic theory. --- Mathematics. --- Operations research. --- Microeconomics. --- Economic Theory/Quantitative Economics/Mathematical Methods. --- Game Theory, Economics, Social and Behav. Sciences. --- Operations Research/Decision Theory. --- Operations Research, Management Science. --- Price theory --- Economics --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Math --- Science --- Economic theory --- Political economy --- Social sciences --- Economic man --- Decision making. --- Management science. --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management decisions --- Choice (Psychology) --- Decision making --- Game theory
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