TY  - BOOK
AU  - Meinhardt,Holger Ingmar
ED  - SpringerLink (Online service)
TI  - The Pre-Kernel as a Tractable Solution for Cooperative Games: An Exercise in Algorithmic Game Theory 
T2  - Theory and Decision Library C, Game Theory, Social Choice, Decision Theory, and Optimization,
SN  - 9783642395499
AV  - HB144 
U1  - 330.0151 23
PY  - 2014///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg, Imprint: Springer
KW  - Economics
KW  - Computer Science
KW  - mathematics
KW  - Economics, Mathematical
KW  - Economics/Management Science
KW  - Game Theory/Mathematical Methods
KW  - Game Theory, Economics, Social and Behav. Sciences
KW  - economic theory
KW  - Math Applications in Computer Science
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/978-3-642-39549-9
ER  -