The Kernel And Bargaining Set For Convex Games PDF Download
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Author | : M. Maschler |
Publisher | : |
Total Pages | : 18 |
Release | : 1967 |
Genre | : Game theory |
ISBN | : |
Download The Kernel and Bargaining Set for Convex Games Book in PDF, ePub and Kindle
Many solution concepts for cooperative games agree or partially agree if the game happens to be convex. For example, convex games have a unique von-Neumann Morgenstern solution which coincides with the core. Also, the (Shapley) value is a center of gravity of the extreme points of the core of a convex game; (namely, the center of gravity when the extreme points are assigned appropriate multiplicities). It is proved in this paper that the kernel (for the grand coalition) of a convex game lies in the relative interior of its core and that the bargaining set (for the grand coalition) coincides with the core. (Author).
Author | : |
Publisher | : |
Total Pages | : 25 |
Release | : 1967 |
Genre | : |
ISBN | : |
Download THE KERNAL AND BARGAINING SET FOR CONVEX GAMES. Book in PDF, ePub and Kindle
In game theory, a convex game is a competitive situation characterized by increasing marginal utility for coalition membership as coalitions grow larger. The core of any n-person game is the set of outcomes that cannot profitably be blocked by a coalition. For the case of convex games, two other solution concepts--the kernel and the bargaining set--prove to be closely related to the core. The kernel lies in the relative interior of the core, and the bargaining set coincides with the core. RM-4571-PR, which introduced the convex game, showed that the core is similarly related to two other solution concepts: the value solution is the center of gravity of the extreme points of the core, and the Von Neumann-Morgenstern stable set solution coincides with the core.
Author | : Rand Corporation |
Publisher | : |
Total Pages | : 35 |
Release | : 1969 |
Genre | : |
ISBN | : |
Download Kernel and Bargaining Set For Convex Games Book in PDF, ePub and Kindle
Author | : Bezalel Peleg |
Publisher | : Springer Science & Business Media |
Total Pages | : 336 |
Release | : 2007-08-15 |
Genre | : Business & Economics |
ISBN | : 3540729453 |
Download Introduction to the Theory of Cooperative Games Book in PDF, ePub and Kindle
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 | : M. Maschler |
Publisher | : |
Total Pages | : 50 |
Release | : 1971 |
Genre | : Economics, Mathematical |
ISBN | : |
Download The Kernal and Bargaining Set for Convex Games Book in PDF, ePub and Kindle
Proof that many solution concepts for convex games either coincide with the core or occupy a central position within the core. The proofs of these results are quite elaborate and require lemmas drawn from various topics of game theory. 50 pp. Ref.
Author | : Nimrod Megiddo |
Publisher | : Springer Science & Business Media |
Total Pages | : 209 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461226481 |
Download Essays in Game Theory Book in PDF, ePub and Kindle
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 | : Holger Ingmar Meinhardt |
Publisher | : Springer Science & Business Media |
Total Pages | : 270 |
Release | : 2013-10-23 |
Genre | : Mathematics |
ISBN | : 364239549X |
Download The Pre-Kernel as a Tractable Solution for Cooperative Games Book in PDF, ePub and Kindle
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 | : Theo S. H. Driessen |
Publisher | : Springer Science & Business Media |
Total Pages | : 235 |
Release | : 2013-03-09 |
Genre | : Business & Economics |
ISBN | : 9401577870 |
Download Cooperative Games, Solutions and Applications Book in PDF, ePub and Kindle
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 | : Andreu Mas-Colell |
Publisher | : Harvard University Press |
Total Pages | : 249 |
Release | : 2016-01-04 |
Genre | : Business & Economics |
ISBN | : 0674728734 |
Download General Equilibrium and Game Theory Book in PDF, ePub and Kindle
Andreu Mas-Colell revolutionized our understanding of competitive markets, price formation, and the behavior of market participants. This volume presents the papers that solidified his standing as one of the preeminent economic theorists of our time. It also is invaluable for anyone wishing to study the craft of a master of economic modeling.
Author | : Dingzhu Du |
Publisher | : Springer Science & Business Media |
Total Pages | : 774 |
Release | : 1998-12-15 |
Genre | : Science |
ISBN | : 9780792352938 |
Download Handbook of combinatorial optimization Book in PDF, ePub and Kindle
This is the second of a multi-volume set. The various volumes deal with several algorithmic approaches for discrete problems as well as with many combinatorial problems. The emphasis is on late-1990s developments. Each chapter is essentially expository in nature, but scholarly in its treatment.