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The Pre-Kernel as a Tractable Solution for Cooperative Games [electronic resource] : An Exercise in Algorithmic Game Theory / by Holger Ingmar Meinhardt.

By: Meinhardt, Holger Ingmar [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Theory and Decision Library C, Game Theory, Social Choice, Decision Theory, and Optimization: 45Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2014Description: XXXIII, 242 p. 8 illus., 3 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783642395499.Subject(s): Computer science -- Mathematics | Game theory | Economic theory | Economics | Game Theory | Game Theory, Economics, Social and Behav. Sciences | Economic Theory/Quantitative Economics/Mathematical Methods | Math Applications in Computer ScienceAdditional physical formats: Printed edition:: No titleDDC classification: 519.3 Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: 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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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.

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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