The paper studies contracting between one principal and N agents in the presence of multilateral externalities. When the principal commits to publicly observed bilateral contracts, inefficiencies arise due to the externalities on agents' reservation utilities. In contrast, when the principal's offers are privately observed, inefficiencies are due to the externalities at efficient outcomes. When the principal can condition her trade with each agent on others' messages, she implements an efficient outcome, while threatening deviators with the harshest possible punishment. However, in the presence of noise that goes to zero more slowly than N goes to infinity, asymptotically agents become nonpivotal, and inefficiency obtains.