One‐seller assignment markets with multi‐unit demands: Core and competitive equilibrium

We consider an assignment market with one seller who owns several indivisible heterogeneous goods and many buyers each willing to buy up to a given capacity. In this market, the core contains the Vickrey payoff vector. However, core allocations may not be supported by competitive equilibrium prices, even in a finite replication of the market. We first characterize the convexity of the associated coalitional game and we show that it is a sufficient condition so that the buyers‐optimal core allocation is competitive. With respect to the seller‐optimal core allocation, we provide a characterization of competitiveness by means of buyers’ valuations. In addition, we characterize in terms of the valuation matrix the coincidence between the core and the set of competitive equilibrium payoff vectors.