The Pre Kernel As A Tractable Solution For Cooperative Games

Author : Holger Ingmar Meinhardt
Publisher : Springer Science & Business Media
Page : 242 pages
File Size : 41,9 Mb
Release : 2013-10-23
Category : Mathematics
ISBN : 9783642395499

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The Pre-Kernel as a Tractable Solution for Cooperative Games by Holger Ingmar Meinhardt Pdf

This present book provides an alternative approach to study the pre-kernel solution of transferable utility games based on a generalized conjugation theory from convex analysis. Although the pre-kernel solution possesses an appealing axiomatic foundation that lets one consider this solution concept as a standard of fairness, the pre-kernel and its related solutions are regarded as obscure and too technically complex to be treated as a real alternative to the Shapley value. Comprehensible and efficient computability is widely regarded as a desirable feature to qualify a solution concept apart from its axiomatic foundation as a standard of fairness. We review and then improve an approach to compute the pre-kernel of a cooperative game by the indirect function. The indirect function is known as the Fenchel-Moreau conjugation of the characteristic function. Extending the approach with the indirect function, we are able to characterize the pre-kernel of the grand coalition simply by the solution sets of a family of quadratic objective functions.

Author : Bezalel Peleg,Peter Sudhölter
Publisher : Springer Science & Business Media
Page : 328 pages
File Size : 44,6 Mb
Release : 2007-08-15
Category : Business & Economics
ISBN : 9783540729457

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Introduction to the Theory of Cooperative Games by Bezalel Peleg,Peter Sudhölter Pdf

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.

Author : Imma Curiel
Publisher : Springer Science & Business Media
Page : 210 pages
File Size : 55,7 Mb
Release : 1997-03-31
Category : Business & Economics
ISBN : 0792344766

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Cooperative Game Theory and Applications by Imma Curiel Pdf

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 : Georgios Chalkiadakis,Edith Elkind,Michael J. Wooldridge
Publisher : Morgan & Claypool Publishers
Page : 171 pages
File Size : 52,8 Mb
Release : 2012
Category : Computers
ISBN : 9781608456529

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Computational Aspects of Cooperative Game Theory by Georgios Chalkiadakis,Edith Elkind,Michael J. Wooldridge Pdf

Cooperative game theory is a branch of (micro-)economics that studies the behavior of self-interested agents in strategic settings where binding agreements among agents are possible. Our aim in this book is to present a survey of work on the computational aspects of cooperative game theory. We begin by formally defining transferable utility games in characteristic function form, and introducing key solution concepts such as the core and the Shapley value. We then discuss two major issues that arise when considering such games from a computational perspective: identifying compact representations for games, and the closely related problem of efficiently computing solution concepts for games. We survey several formalisms for cooperative games that have been proposed in the literature, including, for example, cooperative games defined on networks, as well as general compact representation schemes such as MC-nets and skill games. As a detailed case study, we consider weighted voting games: a widely-used and practically important class of cooperative games that inherently have a natural compact representation. We investigate the complexity of solution concepts for such games, and generalizations of them. We briefly discuss games with non-transferable utility and partition function games. We then overview algorithms for identifying welfare-maximizing coalition structures and methods used by rational agents to form coalitions (even under uncertainty), including bargaining algorithms. We conclude by considering some developing topics, applications, and future research directions.

Author : Roger A McCain
Publisher : World Scientific
Page : 236 pages
File Size : 42,6 Mb
Release : 2013-03-07
Category : Business & Economics
ISBN : 9789814417419

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Value Solutions in Cooperative Games by Roger A McCain Pdf

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. Contents:Value Solutions for Superadditive Transferable Utility Games in Coalition Function FormZeuthen–Nash BargainingNontransferable Utility Games and Games in Partition Function FormA Shapley Value Algorithm for Games in Partition Function FormExtension of the Nucleolus to Nontransferable Utility Games in Partition Function FormA Core Imputation with Variable Bargaining PowerBargaining Power Biform GamesIntertemporal Cooperative Games: A Sketch of a TheoryA Theory of Enterprise Readership: Graduate students and researchers in the field of game theory. Keywords:Cooperative Games;Value;Imputation;Bargaining TheoryKey Features:Proposes a value solution for games of two or more players that: (i) is the Nash bargaining solution in a special case, (ii) allows for unsymmetrical bargaining power, (iii) allows for group-to-group bargaining, and (iv) is always a point in the core of the game if the game is not nullUses methods from mathematical welfare economics to bridge the gap from non-transferable utility to transferable utilityRelying on Biform Games (Brandenburger and Stuart), constructs a model of cooperative value creation in coalitions formed by non-cooperative search and matching

Author : David Mueller,Ralf Trost
Publisher : Springer
Page : 450 pages
File Size : 44,6 Mb
Release : 2017-09-21
Category : Business & Economics
ISBN : 9783319616032

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Game Theory in Management Accounting by David Mueller,Ralf Trost Pdf

This book demonstrates what kind of problems, originating in a management accounting setting, may be solved with game theoretic models. Game theory has experienced growing interest and numerous applications in the field of management accounting. The main focus traditionally has been on the field of non-cooperative behaviour, but the area of cooperative game theory has developed rapidly and has received increasing attention. Intensive research, in combination with the changing culture of publishing, has produced a nearly unmanageable number of publications in the areas concerned. Therefore, one main purpose of this volume is providing an intensive analysis of the intersection of these areas. In addition, the book strengthens the relationship between the theory and the practical applications and it illustrates the two-sided relationship between game theory and management accounting: new game theoretic models offer new fields of applications and these applications raise new questions for the theory.

Author : Anonim
Publisher : Unknown
Page : 984 pages
File Size : 47,5 Mb
Release : 1970
Category : Mathematics
ISBN : UVA:X001409553

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Mathematical Reviews by Anonim Pdf

Author : Zhu Han,Dusit Niyato,Walid Saad,Tamer Başar,Are Hjørungnes
Publisher : Cambridge University Press
Page : 555 pages
File Size : 52,6 Mb
Release : 2012
Category : Business & Economics
ISBN : 9780521196963

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Game Theory in Wireless and Communication Networks by Zhu Han,Dusit Niyato,Walid Saad,Tamer Başar,Are Hjørungnes Pdf

This unified 2001 treatment of game theory focuses on finding state-of-the-art solutions to issues surrounding the next generation of wireless and communications networks. The key results and tools of game theory are covered, as are various real-world technologies and a wide range of techniques for modeling, design and analysis.

Author : Inga Charaja, Juan Jairo
Publisher : KIT Scientific Publishing
Page : 264 pages
File Size : 40,6 Mb
Release : 2021-07-12
Category : Technology & Engineering
ISBN : 9783731510802

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Inverse Dynamic Game Methods for Identification of Cooperative System Behavior by Inga Charaja, Juan Jairo Pdf

This work addresses inverse dynamic games, which generalize the inverse problem of optimal control, and where the aim is to identify cost functions based on observed optimal trajectories. The identified cost functions can describe individual behavior in cooperative systems, e.g. human behavior in human-machine haptic shared control scenarios.

Author : Nimrod Megiddo
Publisher : Springer Science & Business Media
Page : 209 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461226482

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Essays in Game Theory by Nimrod Megiddo Pdf

This volume presents a collection of papers on game theory dedicated to Michael Maschler. Through his dedication and contributions to game theory, Maschler has become an important figure particularly in the area of cooperative games. Game theory has since become an important subject in operations research, economics and management science. As befits such a volume, the main themes covered are cooperative games, coalitions, repeated games, and a cost allocation games. All the contributions are authoritative surveys of a particular topic, so together they will present an invaluable overview of the field to all those working on game theory problems.

Author : V. K . Balakrishnan
Publisher : Courier Corporation
Page : 260 pages
File Size : 44,5 Mb
Release : 2012-04-30
Category : Mathematics
ISBN : 9780486140384

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Introductory Discrete Mathematics by V. K . Balakrishnan Pdf

This concise, undergraduate-level text focuses on combinatorics, graph theory with applications to some standard network optimization problems, and algorithms. More than 200 exercises, many with complete solutions. 1991 edition.

Author : Jacob Engwerda
Publisher : John Wiley & Sons
Page : 514 pages
File Size : 51,9 Mb
Release : 2005-06-17
Category : Business & Economics
ISBN : 0470015241

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LQ Dynamic Optimization and Differential Games by Jacob Engwerda Pdf

Game theory is the theory of social situations, and the majority of research into the topic focuses on how groups of people interact by developing formulas and algorithms to identify optimal strategies and to predict the outcome of interactions. Only fifty years old, it has already revolutionized economics and finance, and is spreading rapidly to a wide variety of fields. LQ Dynamic Optimization and Differential Games is an assessment of the state of the art in its field and the first modern book on linear-quadratic game theory, one of the most commonly used tools for modelling and analysing strategic decision making problems in economics and management. Linear quadratic dynamic models have a long tradition in economics, operations research and control engineering; and the author begins by describing the one-decision maker LQ dynamic optimization problem before introducing LQ differential games. Covers cooperative and non-cooperative scenarios, and treats the standard information structures (open-loop and feedback). Includes real-life economic examples to illustrate theoretical concepts and results. Presents problem formulations and sound mathematical problem analysis. Includes exercises and solutions, enabling use for self-study or as a course text. Supported by a website featuring solutions to exercises, further examples and computer code for numerical examples. LQ Dynamic Optimization and Differential Games offers a comprehensive introduction to the theory and practice of this extensively used class of economic models, and will appeal to applied mathematicians and econometricians as well as researchers and senior undergraduate/graduate students in economics, mathematics, engineering and management science.

Author : Georgios N. Yannakakis,Julian Togelius
Publisher : Springer
Page : 337 pages
File Size : 47,6 Mb
Release : 2018-02-17
Category : Computers
ISBN : 9783319635194

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Artificial Intelligence and Games by Georgios N. Yannakakis,Julian Togelius Pdf

This is the first textbook dedicated to explaining how artificial intelligence (AI) techniques can be used in and for games. After introductory chapters that explain the background and key techniques in AI and games, the authors explain how to use AI to play games, to generate content for games and to model players. The book will be suitable for undergraduate and graduate courses in games, artificial intelligence, design, human-computer interaction, and computational intelligence, and also for self-study by industrial game developers and practitioners. The authors have developed a website (http://www.gameaibook.org) that complements the material covered in the book with up-to-date exercises, lecture slides and reading.

Author : Agoston E. Eiben,J.E. Smith
Publisher : Springer Science & Business Media
Page : 307 pages
File Size : 54,7 Mb
Release : 2013-03-14
Category : Computers
ISBN : 9783662050941

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Introduction to Evolutionary Computing by Agoston E. Eiben,J.E. Smith Pdf

The first complete overview of evolutionary computing, the collective name for a range of problem-solving techniques based on principles of biological evolution, such as natural selection and genetic inheritance. The text is aimed directly at lecturers and graduate and undergraduate students. It is also meant for those who wish to apply evolutionary computing to a particular problem or within a given application area. The book contains quick-reference information on the current state-of-the-art in a wide range of related topics, so it is of interest not just to evolutionary computing specialists but to researchers working in other fields.

Author : Zhi-Long Chen,Nicholas G. Hall
Publisher : Springer Nature
Page : 699 pages
File Size : 44,6 Mb
Release : 2022-02-07
Category : Business & Economics
ISBN : 9783030903749

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Supply Chain Scheduling by Zhi-Long Chen,Nicholas G. Hall Pdf

Supply chain scheduling is a relatively new research area with less than 20 years of history. It is an intersection of two traditional areas: supply chain management and scheduling. In this book, the authors provide a comprehensive coverage of supply chain scheduling. The book covers applications, solution algorithms for solving related problems, evaluation of supply chain conflicts, and models for encouraging cooperation between decision makers. Supply chain scheduling studies detailed scheduling issues within supply chains, as motivated by a variety of applications in the real world. Topics covered by the book include: Coordinated decision making in centralized supply chains, including integrated production and distribution scheduling, joint scheduling and product pricing, and coordinated subcontracting and scheduling. Coordination and competition issues in decentralized supply chains, including conflict and cooperation within scheduling decisions made by different parties in supply chains, and both cooperative and non-cooperative supply chain scheduling games. The book describes a variety of representative problems within each of these topics. The authors define these problems mathematically, describe corresponding applications, and introduce solution methods for solving each problem to improve supply chain performance.