Auction design with shortlisting when value discovery is covert

This paper studies optimal auction design when buyers’ value discovery investment is covert but essential for mutually beneficial trade between seller and buyers. Since selling mechanisms contingent on value discovery (e.g. ex-ante examination fees charged upon information acquisition) are not feasible, we focus mainly on second price auctions with reserves, which can be contingent on the number of actual bidders ex-post. Under a regularity condition of monotone hazard rate, we find that the optimal reserve depends on the number of shortlisted bidders, but for any given shortlist it does not depend on the number of actual bidders. Depending on the value discovery cost, the seller shortlists either the socially efficient number of buyers or one more bidder. The comparison between the two options of the seller is completely resolved. The optimal reserve depends discontinuously and non-monotonically on the value discovery cost. In the former case, equilibrium information acquisition is efficient but ex-post allocation is inefficient, while in the latter case, it is the opposite.