Bayesian implementation and rent extraction in a multi-dimensional procurement problem

We consider a multi-dimensional procurement problem in which sellers have private information about their costs and about a possible design flaw. The information about the design flaw is necessarily correlated. We solve for the optimal Bayesian procurement mechanism that implements the efficient allocation under the constraint that sellers are protected by limited liability. We show that the rents obtained from reporting costs truthfully can be used to reduce the rents sellers must get for reporting the flaw. We compare the optimal Bayesian mechanism to the optimal ex post incentive compatible mechanism that is informationally less demanding.