A generalized assignment game

The game we propose in this paper is a natural extension of the “Assignment Game” of Shapley and Shubik [Shapley, L., Shubik, M., 1972. The assignment game I: the core. International Journal of Game Theory 1, 111–130] to the case where one seller owns a set of different objects instead of only one indivisible object. We prove that the core is nonempty and we study the structure of the set of core payoffs. We endow this set with a lattice structure under the partial ordering of the buyers. We show that, unlike other matching models, we cannot do the same for a dual partial ordering of the sellers.