Extension operators for TU games and the Lovász extension
| Autor: | André Casajus |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Discrete mathematics
Property (philosophy) Applied Mathematics ComputingMilieux_PERSONALCOMPUTING 0211 other engineering and technologies 021107 urban & regional planning Monotonic function 0102 computer and information sciences 02 engineering and technology Extension (predicate logic) 01 natural sciences Operator (computer programming) 010201 computation theory & mathematics Discrete Mathematics and Combinatorics Production (computer science) Indicator vector Mathematics |
| Zdroj: | Discrete Applied Mathematics. 288:66-73 |
| ISSN: | 0166-218X |
| DOI: | 10.1016/j.dam.2020.08.025 |
| Popis: | An extension operator assigns to any TU game its extension, a mapping that assigns a worth to any non-negative resource vector for the players. It satisfies three properties: linearity in the game, homogeneity of extensions, and the extension property. The latter requires the indicator vector of any coalition to be assigned the worth generated by this coalition in the underlying TU game. Algaba et al. (2004) advocate the Lovasz extension (Lovasz, 1983) as a natural extension operator. We show that it is the unique extension operator that satisfies two desirable properties. Resources of players outside a carrier of the game do not affect the worth generated. For monotonic games, extensions are monotonic. Further, we discuss generalizations of the Lovasz extension using CES production functions. |
| Databáze: | OpenAIRE |
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