The Pre-Kernel as a Tractable Solution for Cooperative Games: An Exercise in Algorithmic Game Theory

di Holger Ingmar Meinhardt (Autore)

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, 2016

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.

• Autore: Holger Ingmar Meinhardt
• Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
• Collana: Theory and Decision Library C
• Anno: 2016
• Rilegatura: Paperback / softback
• Pagine: 242 p.
• Dimensioni: 235 x 155 mm
• EAN: 9783662513149

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