Mechanism Design and Non-Cooperative Renegotiation

We characterize decision rules which are implementable in mechanism design settings when, after the play of a mechanism, the uninformed party can propose a new mechanism to the informed party. The necessary and sufficient conditions are, essentially, that the rule be implementable with commitment, that for each type the decision is at least as high as if there were no mechanism, and that the slope of the decision function is not too high. The direct mechanism which implements such a rule with commitment will also implement it in any equilibrium without commitment, so the standard mechanism is robust to renegotiation.