Information structures in optimal auctions

A seller wishes to sell an object to one of multiple bidders. The valuations of the bidders are privately known. We consider the joint design problem in which the seller can decide the accuracy by which bidders learn their valuation and to whom to sell at what price. We establish that optimal information structures in an optimal auction exhibit a number of properties: (i) information structures can be represented by monotone partitions; (ii) the cardinality of each partition is finite; (iii) the partitions are asymmetric across agents. These properties imply that the optimal selling strategy of a seller can be implemented by a sequence of exclusive take-it-or-leave-it offers.