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Journal Article

The Intermediate Set and Limiting Superdi erential for Coalition Games: Between the Core and the Weber Set

Adam Lukáš, Kroupa T.

: International Journal of Game Theory vol.46, 4 (2017), p. 891-918

: GA15-00735S, GA ČR

: coalition game, limiting superdi erential, intermediate set, core, Weber set

: 10.1007/s00182-016-0557-3

: http://library.utia.cas.cz/separaty/2016/MTR/adam-0467365.pdf

(eng): We introduce the intermediate set as an interpolating solution concept between the core and the Weber set of a coalitional game. The new solution is de ned as the limiting superdi erential of the Lov asz extension and thus it completes the hierarchy of variational objects used to represent the core (Fr echet superdi erential) and the Weber set (Clarke superdi erential). It is shown that the intermediate set is a non-convex solution containing the Pareto optimal payo vectors that depend on some chain of coalitions and marginal coalitional contributions with respect to the chain. A detailed comparison between the intermediate set and other set-valued solutions is provided. We compute the exact form of intermediate set for all games and provide its simpli ed characterization for the simple games and the glove game.

: BA

: 10103