Renegotiation proof mechanism design with imperfect type verification

I consider the interaction between an agent and a principal who is unable to commit not to renegotiate. The agent's type only affects the principal's utility. The principal has access to a public signal, correlated with the agent's type, which can be used to (imperfectly) verify the agent's report. I define renegotiation proof mechanisms and characterize the optimal one. The main finding of this paper is that the optimal renegotiation proof mechanism induces pooling at the top, i.e., types above a certain threshold report to be the largest type, while types below the threshold report truthfully.