We show that the Aumann–Davis–Maschler bargaining set and the Mas-Colell bargaining set of a non-leveled NTU game that is either ordinal convex or coalition merge convex coincides with the core of the game. Moreover, we show by means of an example that the foregoing statement may not be valid if the NTU game is marginal convex.
In this paper we propose an extension of the core of NTU games from its domain to a larger set of games satisfying a few conditions of well-behavedness. The solution concept is a rather straightforward generalization of the extended core of TU games introduced by Gomez [2003] and is shown to have similar properties. Also, a set of axioms for solutions of NTU games is presented which characterizes the extended core.
A Cephoid is an algebraic ("Minkowski") sum of finitely many prisms in ℝn. A cephoidal game is an NTU game the feasible sets of which are cephoids. We provide a version of the Shapley NTU value for such games based on the bargaining solution of Maschler–Perles. The value is characterized by a suitable set of axioms
On Bargaining Sets of Convex NTU Games