› › Properties Of Solution Concepts For N Person Cooperative Games

Cooperative Game Theory and Applications

Author : Imma Curiel

Publisher : Springer Science & Business Media

Page : 198 pages

File Size : 12,73 MB

Release : 2013-03-14

Category : Business & Economics

ISBN : 147574871X

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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.



Models in Cooperative Game Theory

Author : Rodica Branzei

Publisher : Springer Science & Business Media

Page : 203 pages

File Size : 23,96 MB

Release : 2008-03-08

Category : Business & Economics

ISBN : 354077954X

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Book Description

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.



The Pre-Kernel as a Tractable Solution for Cooperative Games

Author : Holger Ingmar Meinhardt

Publisher : Springer Science & Business Media

Page : 270 pages

File Size : 18,54 MB

Release : 2013-10-23

Category : Mathematics

ISBN : 364239549X

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Book Description

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.



Cooperative Games, Solutions and Applications

Author : Theo S. H. Driessen

Publisher : Springer Science & Business Media

Page : 235 pages

File Size : 50,29 MB

Release : 2013-03-09

Category : Business & Economics

ISBN : 9401577870

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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.



Introduction to the Theory of Cooperative Games

Author : Bezalel Peleg

Publisher : Springer Science & Business Media

Page : 336 pages

File Size : 49,98 MB

Release : 2007-08-15

Category : Business & Economics

ISBN : 3540729453

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Book Description

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.



Handbook of the Shapley Value

Author : Encarnación Algaba

Publisher : CRC Press

Page : 507 pages

File Size : 24,6 MB

Release : 2019-12-06

Category : Business & Economics

ISBN : 1351241397

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Book Description

Handbook of the Shapley Value contains 24 chapters and a foreword written by Alvin E. Roth, who was awarded the Nobel Memorial Prize in Economic Sciences jointly with Lloyd Shapley in 2012. The purpose of the book is to highlight a range of relevant insights into the Shapley value. Every chapter has been written to honor Lloyd Shapley, who introduced this fascinating value in 1953. The first chapter, by William Thomson, places the Shapley value in the broader context of the theory of cooperative games, and briefly introduces each of the individual contributions to the volume. This is followed by a further contribution from the editors of the volume, which serves to introduce the more significant features of the Shapley value. The rest of the chapters in the book deal with different theoretical or applied aspects inspired by this interesting value and have been contributed specifically for this volume by leading experts in the area of Game Theory. Chapters 3 through to 10 are more focused on theoretical aspects of the Shapley value, Chapters 11 to 15 are related to both theoretical and applied areas. Finally, from Chapter 16 to Chapter 24, more attention is paid to applications of the Shapley value to different problems encountered across a diverse range of fields. As expressed by William Thomson in the Introduction to the book, "The chapters contribute to the subject in several dimensions: Mathematical foundations; axiomatic foundations; computations; applications to special classes of games; power indices; applications to enriched classes of games; applications to concretely specified allocation problems: an ever-widening range, mapping allocation problems into games or implementation." Nowadays, the Shapley value continues to be as appealing as when it was first introduced in 1953, or perhaps even more so now that its potential is supported by the quantity and quality of the available results. This volume collects a large amount of work that definitively demonstrates that the Shapley value provides answers and solutions to a wide variety of problems.



Computational Aspects of Cooperative Game Theory

Author : Georgios Chalkiadakis

Publisher : Morgan & Claypool Publishers

Page : 171 pages

File Size : 37,52 MB

Release : 2012

Category : Computers

ISBN : 1608456528

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Book Description

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.



N-Person Game Theory

Author : Anatol Rapoport

Publisher : Courier Corporation

Page : 337 pages

File Size : 47,25 MB

Release : 2013-06-17

Category : Mathematics

ISBN : 0486143678

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Book Description

DIVSequel to Two-Person Game Theory introduces necessary mathematical notation (mainly set theory), presents basic concepts and models, and provides applications to social situations. /div



Fuzzy and Multiobjective Games for Conflict Resolution

Author : Ichiro Nishizaki

Publisher : Physica

Page : 264 pages

File Size : 50,86 MB

Release : 2013-06-05

Category : Mathematics

ISBN : 3790818305

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Book Description

Decision makers in managerial and public organizations often encounter de cision problems under conflict or competition, because they select strategies independently or by mutual agreement and therefore their payoffs are then affected by the strategies of the other decision makers. Their interests do not always coincide and are at times even completely opposed. Competition or partial cooperation among decision makers should be considered as an essen tial part of the problem when we deal with the decision making problems in organizations which consist of decision makers with conflicting interests. Game theory has been dealing with such problems and its techniques have been used as powerful analytical tools in the resolution process of the decision problems. The publication of the great work by J. von Neumann and O. Morgen stern in 1944 attracted attention of many people and laid the foundation of game theory. We can see remarkable advances in the field of game theory for analysis of economic situations and a number of books in the field have been published in recent years. The aim of game theory is to specify the behavior of each player so as to optimize the interests of the player. It then recommends a set of solutions as strategies so that the actions chosen by each decision maker (player) lead to an outcome most profitable for himself or her self.



Consensus Under Fuzziness

Author : J. Kacprzyk

Publisher : Springer Science & Business Media

Page : 297 pages

File Size : 35,86 MB

Release : 2012-12-06

Category : Business & Economics

ISBN : 146156333X

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Book Description

We live, unfortunately, in turbulent and difficult times plagued by various political, economic, and social problems, as well as by natural disasters worldwide. Systems become more and more complicated, and this concerns all levels, exemplified first by global political alliances, groups of countries, regions, etc., and secondly, by multinational (global) corporations and companies of all sizes. These same concerns affect all social groups. This all makes decision processes very complicated. In virtually all decision processes in these complicated systems, there are various actors (decision makers) who represent individual subjects (persons, countries, companies, etc.) and their respective interest groups. To reach a meaningful (good) decision, opinions of all such actors must be taken into account or a given decision may be rejected and not implemented. Ideally, a decision would be made after a consensus between the parties involved had been attained. So, consensus is a very desirable situation. In most real-world cases there is considerable uncertainty concerning all aspects of the decision making process. Moreover, opinions, goals, constraints, etc. are usually imprecisely known. This makes the decision making process difficult as one cannot employ conventional "hard" tools.