The Pre-Kernel as a Tractable Solution for Cooperative Games :
Meinhardt, Holger Ingmar.
The Pre-Kernel as a Tractable Solution for Cooperative Games : An Exercise in Algorithmic Game Theory / by Holger Ingmar Meinhardt. - xxxiii, 242 páginas 8 ilustraciones, 3 ilustraciones en color. recurso en línea. - Theory and Decision Library C, Game Theory, Social Choice, Decision Theory, and Optimization, 45 0924-6126 ; .
Springer eBooks
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.
9783642395499
10.1007/9783642395499 doi
HB144
The Pre-Kernel as a Tractable Solution for Cooperative Games : An Exercise in Algorithmic Game Theory / by Holger Ingmar Meinhardt. - xxxiii, 242 páginas 8 ilustraciones, 3 ilustraciones en color. recurso en línea. - Theory and Decision Library C, Game Theory, Social Choice, Decision Theory, and Optimization, 45 0924-6126 ; .
Springer eBooks
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.
9783642395499
10.1007/9783642395499 doi
HB144