The Pre-Kernel as a Tractable Solution for Cooperative Games
An Exercise in Algorithmic Game Theory
Nonfiction, Science & Nature, Mathematics, Game Theory, Business & Finance, Economics, Theory of Economics
| Author: | Holger Ingmar Meinhardt | ISBN: | 9783642395499 |
| Publisher: | Springer Berlin Heidelberg | Publication: | October 23, 2013 |
| Imprint: | Springer | Language: | English |
| Author: | Holger Ingmar Meinhardt |
| ISBN: | 9783642395499 |
| Publisher: | Springer Berlin Heidelberg |
| Publication: | October 23, 2013 |
| Imprint: | Springer |
| Language: | English |
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.
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.
