Efficient and optimal selling procedures with private information acquisition costs

In auctions with private information acquisition costs, we completely characterize efficient and optimal two-stage selling procedures, with the first stage being the prescreening or entry right allocation mechanism, and the second stage being the traditional private good provision mechanism. Both efficiency and optimality require the second stage mechanism to be ex post efficient. For the first stage of entry allocation, both efficient and optimal mechanisms admit the most efficient bidders (the bidders with the least information acquisition costs), while the optimal mechanism admits fewer entrants. The efficient entry right allocation rule maximizes the expected total surplus, while the optimal entry right allocation rule maximizes the expected "virtual" total surplus, which is the total surplus adjusted for the information rent. We show that both efficient and optimal entry right allocation rules can be truthfully implemented in dominant strategies. We also demonstrate that the optimal entry right allocation mechanism can be implemented through an all-pay auction.