When do incomplete contracts matter?

This paper derives conditions under which the introduction of a third-party agent solves the renegotiation-proofness problem of Moore and Repullo (1988)-type mechanisms, without introducing the potential for other agents to collude with the third-party. The key novelties of our mechanism are: (i) the introduction of a third-party agent only off-equilibrium and with some probability; (ii) the fact that both its existence and its identity are unknown to the other agents. We show that under these conditions, which are satisfied in many empirical applications, a hidden third-party agent can restore the implementation of the efficient allocation. If this agent does not observe the state of the world, we provide a sufficient condition for implementation to succeed