Renegotiation-proof mechanism design

We study a mechanism design problem under the assumption that renegotiation cannot be prevented. We investigate what kind of equilibria of which mechanisms are renegotiation-proof under a variety of renegotiation procedures, and which social choice functions can be implemented in a way that is renegotiation-proof. In complete information environments, we show that the set of ex post renegotiation- roof implementable social choice functions contains all ex post efficient allocations when there at least three agents, but only budget balanced Groves allocations when there are two agents. In incomplete information environments with correlated beliefs and at least three agents, every ex post efficient social choice function can be implemented in the presence of ex post renegotiation, but with independent private values only social choice functions that are given by budget balanced Groves in expectations mechanisms are implementable in such a way. We further show that the requirement of interim renegotiation-proofness does not impose additional restrictions on implementable social choice functions under complete information, but is likely to impose additional restrictions under incomplete information.