Article ID: | iaor20073076 |
Country: | Netherlands |
Volume: | 61 |
Issue: | 1 |
Start Page Number: | 156 |
End Page Number: | 171 |
Publication Date: | Feb 2007 |
Journal: | Statistica Neerlandica |
Authors: | Vermeulen Dries, Morales Dolores Romero, Lok Reinder B. |
For the allocation of heterogeneous items, it is known that the buyers-are-substitutes condition is necessary and sufficient to ensure that a pricing equilibrium can yield the same allocation and payments as the VCG mechanism. Furthermore, concavity of the corresponding transferable utility (TU)-game guarantees that this VCG outcome can also be achieved by an ascending price auction. We show that concavity, and hence the buyers-are-substitutes condition, holds for the TU-game of the assignment problem with general capacities. Therefore, the VCG mechanism is supported by a pricing equilibrium which can also be achieved by an ascending auction. We also show that the buyers-are-substitutes condition, and hence concavity, does not hold anymore for very natural and straightforward extensions of this problem. This shows that the necessity of the substitutes property is a considerable restriction on the applicability of the VCG mechanism.