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

0467365 - ÚTIA 2018 RIV CH eng J - Journal Article
Adam, Lukáš - Kroupa, T.
The Intermediate Set and Limiting Superdi erential for Coalition Games: Between the Core and the Weber Set.
International Journal of Game Theory. Roč. 46, č. 4 (2017), s. 891-918. ISSN 0020-7276. E-ISSN 1432-1270
R&D Projects: GA ČR GA15-00735S
Institutional support: RVO:67985556
Keywords : coalition game * limiting superdi erential * intermediate set * core * Weber set
OECD category: Statistics and probability
Impact factor: 0.500, year: 2017
http://library.utia.cas.cz/separaty/2016/MTR/adam-0467365.pdf

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.
Permanent Link: http://hdl.handle.net/11104/0266441