International Journal of Game Theory

, Volume 46, Issue 4, pp 891–918 | Cite as

The intermediate set and limiting superdifferential for coalitional games: between the core and the Weber set

  • Lukáš Adam
  • Tomáš Kroupa
Original Paper


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 defined as the limiting superdifferential of the Lovász extension and thus it completes the hierarchy of variational objects used to represent the core (Fréchet superdifferential) and the Weber set (Clarke superdifferential). It is shown that the intermediate set is a non-convex solution containing the Pareto optimal payoff 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 simplified characterization for the simple games and the glove game.


Coalitional game Limiting superdifferential Intermediate set Core Weber set 

Mathematics Subject Classification

91A12 49J52 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institute of Information Theory and AutomationCzech Academy of SciencesPragueCzech Republic
  2. 2.Dipartimento di Matematica “Federigo Enriques”Università degli Studi di MilanoMilanItaly

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