The nucleolus and the core-center of multi-sided Böhm-Bawerk assignment markets

We prove that both the nucleolus and the core-center, i.e., the mass center of the core, of an m-sided Böhm-Bawerk assignment market can be respectively computed from the nucleolus and the core-center of a convex game defined on the set of m sectors. What is more, in the calculus of the nucleolus of this latter game only singletons and coalitions containing all agents but one need to be taken into account. All these results simplify the computation of the nucleolus and the core-center of a multi-sided Böhm-Bawerk assignment market with a large number of agents. As a consequence we can show that, contrary to the bilateral case, for multi-sided Böhm-Bawerk assignment markets the nucleolus and the core-center do not coincide in general.