The Pre-Kernel as a Tractable Solution for Cooperative Games
Produktnummer:
18b91fde6b955448af86c7bf78344bfc9f
| Autor: | Meinhardt, Holger Ingmar |
|---|---|
| Themengebiete: | Convex Analysis Cooperative Game Theory Fair Division Fairness Fenchel-Moreau Conjugation Pre-Kernel Solutions |
| Veröffentlichungsdatum: | 07.11.2013 |
| EAN: | 9783642395482 |
| Sprache: | Englisch |
| Seitenzahl: | 242 |
| Produktart: | Gebunden |
| Verlag: | Springer Berlin |
| Untertitel: | An Exercise in Algorithmic Game Theory |
Produktinformationen "The Pre-Kernel as a Tractable Solution for Cooperative Games"
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.
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