A note on competitive prices in multilateral assignment markets

A multilateral assignment market with buyers and a number of different types of firms can be modeled by a multi-sided assignment game. We prove that core allocations of the latter are in a one-to-one correspondence with competitive prices of the former, where the notion of competitive price extends that of Roth and Sotomayor (1990). This result generalizes to multi-sided assignment markets the characterization of competitive prices known for the two-sided case.