$$k$$ k -core covers and the core
| Autor: | M. G. Fiestras-Janeiro, Manuel A. Mosquera, Estela Sánchez-Rodríguez, Arantza Estévez-Fernández, Peter Borm |
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| Přispěvatelé: | Econometrics and Operations Research, Research Group: Operations Research |
| Rok vydání: | 2015 |
| Předmět: |
1207.06 Teoría de Juegos
Computer Science::Computer Science and Game Theory SDG 16 - Peace General Mathematics Management Science and Operations Research Type (model theory) Assignment games Combinatorics Integer k-compromise admissibility k-core cover k-compromise stability Transferable utility Mathematics Core cover SDG 16 - Peace Justice and Strong Institutions Stochastic game ComputingMilieux_PERSONALCOMPUTING Extension (predicate logic) Justice and Strong Institutions Core (game theory) Cover (topology) Bounded function Core Mathematical economics Software |
| Zdroj: | Sanchez-Rodriguez, E, Borm, P, Estevez Fernandez, M A, Fiestras-Janeiro, M G & Mosquera, M A 2015, ' k-core covers and the core ', Mathematical Methods of Operations Research, vol. 81, no. 2, pp. 147-167 . https://doi.org/10.1007/s00186-014-0490-9 Investigo. Repositorio Institucional de la Universidade de Vigo Universidade de Vigo (UVigo) Mathematical Methods of Operations Research, 81(2), 147-167. Physica-Verlag Mathematical Methods of Operations Research, 81(2), 147-167. SPRINGER HEIDELBERG |
| ISSN: | 1432-5217 1432-2994 |
| DOI: | 10.1007/s00186-014-0490-9 |
| Popis: | This paper extends the notion of individual minimal rights for a transferable utility game (TU-game) to coalitional minimal rights using minimal balanced families of a specific type, thus defining a corresponding minimal rights game. It is shown that the core of a TU-game coincides with the core of the corresponding minimal rights game. Moreover, the paper introduces the notion of the $$k$$k-core cover as an extension of the core cover. The $$k$$k-core cover of a TU-game consists of all efficient payoff vectors for which the total joint payoff for any coalition of size at most $$k$$k is bounded from above by the value of this coalition in the corresponding dual game, and from below by the value of this coalition in the corresponding minimal rights game. It is shown that the core of a TU-game with player set $$N$$N coincides with the largest integer below or equal to $$\frac{|N|}{2}$$|N|2-core cover. Furthermore, full characterizations of games for which a $$k$$k-core cover is nonempty and for which a $$k$$k-core cover coincides with the core are provided. |
| Databáze: | OpenAIRE |
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