Auctions design with private costs of valuation discovery

This paper extends the pre-bid R&D and auctions design literature to an independent private value setting where each bidder incurs a private-information valuation discovery cost upon entry. The seller commits to a mechanism before the bidders' entry decisions. The main findings are as follows. Firstly, a second-price auction with no entry fee and a reserve price equal to seller's valuation is ex ante efficient. Secondly, a second price auction with the same reserve price and appropriate ex ante entry fees is revenue-maximizing. Every bidder's ex ante entry fee equals the hazard rate of his entry cost distribution, evaluated at the desired entry-threshold for him. Thirdly, the revenue-maximizing entry differs from the ex ante efficient entry. Fourthly, even for the symmetric setting, the ex ante efficient/revenue-maximizing entry could be asymmetric. Lastly, for the symmetric setting, when the cumulative distribution function of the entry costs changes rather slowly with respect to its argument, the efficient entry must be symmetric across bidders and it is the unique entry equilibrium of the efficient auction. If the hazard rate of the entry cost distribution is additionally increasing, then the revenue-maximizing entry must also be symmetric and it is the unique entry equilibrium of the revenue-maximizing auction. These results mean that large dispersion in the entry costs restores the symmetry in the efficient/revenue-maximizing entry.