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Extension operators for TU games and the Lovász extension

  • 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 Lovász extension (Lovász, 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 Lovász extension using CES production functions.

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Document Type:Article
Author:André Casajus
Chairs and Professorships:Chair of Economics and Information Systems
Parent Title (English):Discrete Applied Mathematics
Year of Completion:2021
First Page:66
Last Page:73
Tag:CES production function; Lovász extension; TU game
Content Focus:Academic Audience
Peer Reviewed:Yes
Rankings:AJG Ranking / 2
VHB Ranking / A
SJR Ranking / Q2
Licence (German):License LogoUrheberrechtlich geschützt