Core and pricing equilibria in combinatorial exchanges

We study assignment problems where individuals trade packages consisting of several objects. In a seminal paper Bikhchandani and Ostroy (2002) have shown that the efficient assignments can be formulated as a linear programming problem. The pricing equilibria introduced by them do not always fill out the core in a combinatorial exchange. We introduce a linear programming formulation where we can easily identify in the dual problem whether the core is empty, and for which the pricing equilibrium always coincides with the core when it is not empty.