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

Author: Meinhardt, Holger Ingmar

Brand: Springer

Edition: 2014

Number Of Pages: 275

EAN: 9783642395482

Release Date: 07-11-2013

Package Dimensions: 9.2 x 6.2 x 0.8 inches

Languages: English

Binding: Hardcover

Part Number: 5 black & white illustrations, 3 colour

Details: 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.