Cooperative Game Theory and Applications PDF Download

Author: Imma Curiel
Publisher: Springer Science & Business Media
ISBN: 147574871X
Category : Business & Economics
Languages : en
Pages : 198

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Book Description
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.

Author: Julia Drechsel
Publisher: Springer Science & Business Media
ISBN: 3642137253
Category : Business & Economics
Languages : en
Pages : 175

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Book Description
The presented work combines two areas of research: cooperative game theory and lot size optimization. One of the most essential problems in cooperations is to allocate cooperative profits or costs among the partners. The core is a well known method from cooperative game theory that describes efficient and stable profit/cost allocations. A general algorithm based on the idea of constraint generation to compute core elements for cooperative optimization problems is provided. Beside its application for the classical core, an extensive discussion of core variants is presented and how they can be handled with the proposed algorithm. The second part of the thesis contains several cooperative lot sizing problems of different complexity that are analyzed regarding theoretical properties like monotonicity or concavity and solved with the proposed row generation algorithm to compute core elements; i.e. determining stable and fair cost allocations.

Author: Jesús Mario Bilbao
Publisher: Springer
ISBN: 9780792377825
Category : Business & Economics
Languages : en
Pages : 326

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Book Description
The aim of Cooperative Games on Combinatorial Structures is to analyze conflict situations in which two or more players can make coalitions and obtain prizes and penalties. This approach to situations of competition and cooperation was given in the seminal treatise by John von Neumann and Oskar Morgenstern, Theory of Games and Economic Behavior. Cooperative game theory has succeeded in providing many applications of game theory. In this volume, games defined on combinatorial structures will be analyzed, i.e. a set system over a set of players. In many situations the author will work in a closure space. Examples of closure operators are the spanning operator of linear algebra and all convex hull operators. Chapters 1-4 constitute a review of mathematical concepts from Cooperative Game Theory, Graph Theory, Linear and Integer Programming, Combinatorial Optimization, Discrete Convex Analysis and Computational Complexity. The table of contents is a short guide to the topics and methods covered in this book. In Chapters 11 and 12, several notebooks are presented with the system Mathematica by Wolfram in the contexts of the packages DiscreteMath (Skiena) and Cooperative (Carter). There will also be found in the book several research projects. These are intended to offer new ideas that the reader should consider with caution. This book will be of interest to graduate students with some experience in game theory or mathematical programming and professional researchers in game theory, operational research and its applications in economic theory, and the political and social sciences. In addition, it will be especially useful for professionals who are interested in models for understanding and managing conflicts: management and operational research scientists, political and military scientists, and professional negotiators.

Author: Martin Shubik
Publisher: Princeton University Press
ISBN: 1400877385
Category : Business & Economics
Languages : en
Pages : 498

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Book Description
Professor Morgenstern's deep interests in economic time series and problems of measurement are represented by path-breaking articles devoted to the application of modern statistical analysis to temporal economic data. Originally published in 1967. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author: Theo S. H. Driessen
Publisher: Springer Science & Business Media
ISBN: 9401577870
Category : Business & Economics
Languages : en
Pages : 235

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Book Description
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.

Author: Vitor Balestro
Publisher: Springer Nature
ISBN: 3031505077
Category :
Languages : en
Pages : 1195

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Author: Bor-Luh Lin
Publisher: CRC Press
ISBN: 1000942325
Category : Mathematics
Languages : en
Pages : 340

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Book Description
This book contains expanded versions of the talks given at the conference held in honour of professor Ky Fan in California in 1985, as well as papers on nonlinear and convex analysis as contributions to Ky Fan. It also includes a list of publications by Ky Fan.

Author: Alberto Cambini
Publisher:
ISBN:
Category : Convex functions
Languages : en
Pages : 416

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Book Description
The aim of this volume is to strengthen the interest in generalized convexity, generalized monotonicity and related areas and to stimulate new research in these fields by update survey (or recent results) of known experts covering many important topics such as some new theoretical aspects of generalized convexity and generalized invexity, some applications of generalized monotonicity and pseudomonotonicity to equilibrium problems and to economic and financial problems, some applications of abstract convexity, some applications of discrete convex analysis to cooperative game theory, fractional programming, optimality conditions in vector optimization (smooth and non-smooth), semi-infinite optimization and a new method for solving multiobjective problems.

Author: Jean-Pierre Aubin
Publisher: Springer Science & Business Media
ISBN: 3662035391
Category : Mathematics
Languages : en
Pages : 442

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Book Description
Progress in the theory of economic equilibria and in game theory has proceeded hand in hand with that of the mathematical tools used in the field, namely nonlinear analysis and, in particular, convex analysis. Jean-Pierre Aubin, one of the leading specialists in nonlinear analysis and its application to economics, has written a rigorous and concise - yet still elementary and self-contained - textbook providing the mathematical tools needed to study optima and equilibria, as solutions to problems, arising in economics, management sciences, operations research, cooperative and non-cooperative games, fuzzy games etc. It begins with the foundations of optimization theory, and mathematical programming, and in particular convex and nonsmooth analysis. Nonlinear analysis is then presented, first game-theoretically, then in the framework of set valued analysis. These results are then applied to the main classes of economic equilibria. The book contains numerous exercises and problems: the latter allow the reader to venture into areas of nonlinear analysis that lie beyond the scope of the book and of most graduate courses.

Author: Toru Maruyama
Publisher: Springer Science & Business Media
ISBN: 364248719X
Category : Mathematics
Languages : en
Pages : 303

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Book Description
The papers collected in this volume are contributions to T.I.Tech./K.E.S. Conference on Nonlinear and Convex Analysis in Economic Theory, which was held at Keio University, July 2-4, 1993. The conference was organized by Tokyo Institute of Technology (T. I. Tech.) and the Keio Economic Society (K. E. S.) , and supported by Nihon Keizai Shimbun Inc .. A lot of economic problems can be formulated as constrained optimiza tions and equilibrations of their solutions. Nonlinear-convex analysis has been supplying economists with indispensable mathematical machineries for these problems arising in economic theory. Conversely, mathematicians working in this discipline of analysis have been stimulated by various mathematical difficulties raised by economic the ories. Although our special emphasis was laid upon "nonlinearity" and "con vexity" in relation with economic theories, we also incorporated stochastic aspects of financial economics in our project taking account of the remark able rapid growth of this discipline during the last decade. The conference was designed to bring together those mathematicians who were seriously interested in getting new challenging stimuli from economic theories with those economists who were seeking for effective mathematical weapons for their researches. Thirty invited talks (six of them were plenary talks) given at the conf- ence were roughly classified under the following six headings : 1) Nonlinear Dynamical Systems and Business Fluctuations, . 2) Fixed Point Theory, 3) Convex Analysis and Optimization, 4) Eigenvalue of Positive Operators, 5) Stochastic Analysis and Financial Market, 6) General Equilibrium Analysis.