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The Intermediate Set and Limiting Superdifferential for Coalition Games: Between the Core and the Weber Set
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 Lovasz extension and thus it
completes the hierarchy of variational objects used to represent the core
(Frechet 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.Comment: Submitted to International Journal of Game Theor