This paper considers auction environments with a (possibly correlated) common prior over bidders' values, where each bidder may have additional information (e.g., through information acquisition). Under certain conditions, we characterize the optimal mechanisms in terms of the expected revenue that is guaranteed given whatever additional information is available to the bidders. Even if the values are correlated,we do not necessarily have full-surplus extraction, and moreover, the optimal mechanism resembles those in the independently distributed cases. Specifically, we show that (i) a second-price auction is optimal among all the efficient mechanisms, and (ii) it is rate-optimal among all the mechanisms
