The Pre Kernel As A Tractable Solution For Cooperative Games PDF Download
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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 | : 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 | : C. Chang |
Publisher | : |
Total Pages | : 8 |
Release | : 1994 |
Genre | : |
ISBN | : |
Download (Pre)kernel Catchers for Cooperative Games Book in PDF, ePub and Kindle
Author | : Imma Curiel |
Publisher | : Springer Science & Business Media |
Total Pages | : 210 |
Release | : 1997-03-31 |
Genre | : Business & Economics |
ISBN | : 9780792344766 |
Download Cooperative Game Theory and Applications Book in PDF, ePub and Kindle
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 |
Publisher | : Morgan & Claypool Publishers |
Total Pages | : 171 |
Release | : 2012 |
Genre | : Computers |
ISBN | : 1608456528 |
Download Computational Aspects of Cooperative Game Theory Book in PDF, ePub and Kindle
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 | : Michael Maschler |
Publisher | : |
Total Pages | : 63 |
Release | : 1965 |
Genre | : |
ISBN | : |
Download The Structure of the Kernel of a Cooperative Game Book in PDF, ePub and Kindle
A study of the kernel of a cooperative game. In this paper the authors derive a procedure for the players which, if abided by, leads to an outcome in the kernel. Moreover, each outcome in the kernel can be reached by this procedure. The procedure consists of a set of three rules and involves the formation of 'intermediate coalitions' which play 'intermediate games, ' after which the members of each intermediate coalition play a 'reduced game' to decide the share of their spoils. The procedure is further analyzed in the case of monotonic games and in the case of simple games, and the results that are obtained reduce considerably the amount of computation which is needed to compute the kernels of such games. In particular, they compute the kernel of the 7-person projective game (for the grand coalition), which is a star consisting of seven straight-line segments connecting the center to the points of the main simple solution. Finally, conditions under which modifications of the characteristic function do not change its kernel are presented. (Author).
Author | : Kai Michaelis |
Publisher | : |
Total Pages | : 350 |
Release | : 1982 |
Genre | : Decision making |
ISBN | : |
Download On the Nature of Solution Concepts for Cooperative Games Book in PDF, ePub and Kindle
Author | : Kensaku Kikuta |
Publisher | : |
Total Pages | : 0 |
Release | : 1998 |
Genre | : |
ISBN | : |
Download The Kernel for Reasonable Outcomes in a Cooperative Game Book in PDF, ePub and Kindle
It is shown that the prekernel and the pre-nucleolus of a cooperative game coincide with the kernel and the nucleolus for the reasonable set of the game respectively.
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 | : Xia Zhang |
Publisher | : |
Total Pages | : |
Release | : 2021 |
Genre | : |
ISBN | : |
Download The Prekernel of Cooperative Games with Alpha-excess Book in PDF, ePub and Kindle
In this paper, we introduce a new approach to measure the dissatisfaction for coalitions of players in cooperative transferable utility games. This is done by considering affine (and convex) combinations of the classical excess and the proportional excess. Based on this so-called alpha-excess, we define new solution concepts for cooperative games, such as the alpha-prenucleolus and the alpha-prekernel. The classical prenucleolus and prekernel are a special case. We characterize the alpha-prekernel by strong stability and the alpha-balanced surplus property. Also, we show that the payoff vector generated by the alpha-prenucleolus belongs to the alpha-prekernel.