Optimal VCG Mechanisms to Assign Multiple Tasks∗

We develop optimal VCG mechanisms in order to assign identical economic “bads” (for example, costly tasks) to agents. The optimal non-deficit VCG mechanism achieves asymptotic budget balance, yet the non-deficit requirement is incompatible with reasonable welfare bounds. If we omit the non-deficit requirement, individual rationality greatly changes the relationship between burning a budget surplus and financing a budget deficit. Allowing a slight deficit, the optimal individually rational VCG mechanism becomes asymptotically budget balanced more easily. Such a phenomenon cannot be found in the case of assigning economic “goods.”