Contracting with Externalities

The paper studies inefficiencies arising in contracting between one principal and N agents when the utility of each agent depends on all agents' trades with the principal. When the principal commits to a set of publicly observable bilateral contract offers, the arising inefficiency is due entirely to the externalities imposed on non-signers. In contrast, when the principal's offers are privately observed, the distortion is due to the externalities given agents' equilibrium trades. Comparison of the two externalities determines the relative efficiency of the two contracting regimes. In both cases, we show that when N is large, each agent can be treated as non-pivotal, provided that appropriate continuity assumptions are satisfied. We also study the case in which the principal can condition each agent's trade on other agents' messages. We characterize the set of such mechanisms in which each agent's participation is voluntary. When the principal can commit to any such mechanism, she implements the first-best outcome, while threatening each deviator with the harshest possible punishment. However, in the presence of noise that goes to zero slower than N goes to infinity, in the limit we obtain a (generally inefficient) outcome in which each agent feels non-pivotal.