The Pre-Kernel as a Tractable Solution for Cooperative Games: An Exercise in Algorithmic Game Theory
ISBN/ASIN: 9783642395482,9783642395499 | 2014 | English | pdf | 242/270 pages | 2.32 Mb
Publisher: Springer-Verlag Berlin Heidelberg | Author: Holger Ingmar Meinhardt (auth.) | Edition: 1
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.