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The Pre-Kernel as a Tractable Solution for Cooperative Games: An Exercise in Algorithmic Game Theory: Theory and Decision Library C, cartea 45

Autor Holger Ingmar Meinhardt
en Limba Engleză Hardback – 7 noi 2013
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.
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Specificații

ISBN-13: 9783642395482
ISBN-10: 3642395481
Pagini: 276
Ilustrații: XXXIII, 242 p. 8 illus., 3 illus. in color.
Dimensiuni: 155 x 235 x 20 mm
Greutate: 0.52 kg
Ediția:2014
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Theory and Decision Library C

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

Introduction.- Some Solution Schemes and Game Properties.- The Shapley Value and (Pre-Kernel) as a Fairness Concept.- Fair Division in Cournot Markets.- Some Preliminary Results.- A Pre-Kernel Characterization and Orthogonal Projection.- Characterization of the Pre-Kernel by Solution Sets.- Algorithms for Computing the Pre-Kernel.- An Upper Dimension Bound of the Pre-Kernel.- Concluding Remarks.

Notă biografică

Dr. Holger Meinhardt is a Senior Research Affiliate at Karlsruhe Institute of Technology (KIT).

Textul de pe ultima copertă

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.

Caracteristici

Characterizes a fair division rule of game theory by convex analysis Proposes tractable formula to solve fair division problems in real life situations Provides algorithms to implement vectorized and parallel computer programs designed to solve fair division problems? Includes supplementary material: sn.pub/extras