Information acquisition and efficient mechanism design

We consider a general mechanism design setting where each agent can acquire (covert) information before participating in the mechanism. The central question is whether a mechanism exists that provides the efficient incentives for information acquisition ex-ante and implements the efficient allocation conditional on the private information ex-post. It is shown that in every private value environment the Vickrey-Clark-Groves mechanism guarantees both ex-ante as well as ex-post efficiency. In contrast, with common values, ex-ante and ex-post efficiency cannot be reconciled in general. Sufficient conditions in terms of sub- and supermodularity are provided when (all) ex-post efficient mechanisms lead to private under- or over-acquisition of information.