This book introduces new concepts for cooperative game theory, and particularly solutions that determine the distribution of a coalitional surplus among the members of the coalition. It also addresses several generalizations of cooperative game theory. Drawing on methods of welfare economics, new value solutions are derived for Non-Transferable Utility games with and without differences of bargaining power among the members of the coalition. Cooperation in intertemporal games is examined, and conditions that permit the reduction of these games to games in coalition function form are outlined. Biform games and games that combine non-cooperative search and matching of coalition members with cooperative solutions (i.e., efficient contracts) within the coalition are considered.

The study of the theory of games was started in Von Neumann (1928), but the development of the theory of games was accelerated after the publication of the classical book "Theory of games and economic behavior" by Von Neumann and Morgenstern (1944). As an initial step, the theory of games aims to put situations of conflict and cooperation into mathematical models. In the second and final step, the resulting models are analysed on the basis of equitable and mathematical reasonings. The conflict and/or cooperative situation in question is generally due to the interaction between two or more individuals (players). Their interaction may lead up to several potential payoffs over which each player has his own preferences. Any player attempts to achieve his largest possible payoff, but the other players may also exert their influence on the realization of some potential payoff. As already mentioned, the theory of games consists of two parts, a modelling part and a solution part. Concerning the modelling part, the mathematical models of conflict and cooperative situations are described. The description of the models includes the rules, the strategy space of any player, potential payoffs to the players, the preferences of each player over the set of all potential payoffs, etc. According to the rules, it is either permitted or forbidden that the players communicate with one another in order to make binding agreements regarding their mutual actions.

This book systematically presents the main solutions of cooperative games: the core, bargaining set, kernel, nucleolus, and the Shapley value of TU games as well as the core, the Shapley value, and the ordinal bargaining set of NTU games. The authors devote a separate chapter to each solution, wherein they study its properties in full detail. In addition, important variants are defined or even intensively analyzed.

This book introduces new concepts for cooperative game theory, and particularly solutions that determine the distribution of a coalitional surplus among the members of the coalition. It also addresses several generalizations of cooperative game theory. Drawing on methods of welfare economics, new value solutions are derived for Non-Transferable Utility games with and without differences of bargaining power among the members of the coalition. Cooperation in intertemporal games is examined, and conditions that permit the reduction of these games to games in coalition function form are outlined. Biform games and games that combine non-cooperative search and matching of coalition members with cooperative solutions (i.e., efficient contracts) within the coalition are considered.

This book proposes several commonly used interval-valued solution concepts of interval-valued cooperative games with transferable utility. It thoroughly investigates these solutions, thereby establishing the properties, models, methods, and applications. The first chapter proposes the interval-valued least square solutions and quadratic programming models, methods, and properties. Next, the satisfactory-degree-based non-linear programming models for computing interval-valued cores and corresponding bisection algorithm are explained. Finally, the book explores several simplification methods of interval-valued solutions: the interval-valued equal division and equal surplus division values; the interval-valued Shapley, egalitarian Shapley, and discounted Shapley values; the interval-valued solidarity and generalized solidarity values; and the interval-valued Banzhaf value. This book is designed for individuals from different fields and disciplines, such as decision science, game theory, management science, operations research, fuzzy sets or fuzzy mathematics, applied mathematics, industrial engineering, finance, applied economics, expert system, and social economy as well as artificial intelligence. Moreover, it is suitable for teachers, postgraduates, and researchers from different disciplines: decision analysis, management, operations research, fuzzy mathematics, fuzzy system analysis, applied mathematics, systems engineering, project management, supply chain management, industrial engineering, applied economics, and hydrology and water resources.

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.

This book constitutes extended, revised and selected papers from the Third East Asia Game Theory International Conference, EAGT 2019, held in Fuzhou, China, in March 2019. The 10 full papers presented in this volume were carefully reviewed and selected from a total of 146 submissions. The papers in the volume are focused on non-cooperative and cooperative games and cover such subjects or disciplines as game theory, operations research, mathematics, decision science, management science, economics, experiment economics, system engineering, psychology and control theory.

For several decades, scholars have developed methods for solving optimization problems which emerge in economics, econometrics, operations research, and other disciplines. A considerable effort has been made to construct equations from which constraints can be derived, but surprisingly little has been done to construct the other part of optimization models: the scalar-valued objective function, the constrained maximum or minimum of which gives the optimal solution. The given volume is intended to attract attention to the problem, to present the major achievements in the field and to stimulate further research and teaching.

In this book applications of cooperative game theory that arise from combinatorial optimization problems are described. It is well known that the mathematical modeling of various real-world decision-making situations gives rise to combinatorial optimization problems. For situations where more than one decision-maker is involved classical combinatorial optimization theory does not suffice and it is here that cooperative game theory can make an important contribution. If a group of decision-makers decide to undertake a project together in order to increase the total revenue or decrease the total costs, they face two problems. The first one is how to execute the project in an optimal way so as to increase revenue. The second one is how to divide the revenue attained among the participants. It is with this second problem that cooperative game theory can help. The solution concepts from cooperative game theory can be applied to arrive at revenue allocation schemes. In this book the type of problems described above are examined. Although the choice of topics is application-driven, it also discusses theoretical questions that arise from the situations that are studied. For all the games described attention will be paid to the appropriateness of several game-theoretic solution concepts in the particular contexts that are considered. The computation complexity of the game-theoretic solution concepts in the situation at hand will also be considered.

"Deals with real life situations where objectives of the participants are partially cooperative and partially conflicting"--