Optimal Auctions with Participation Costs

We study the optimal auction problem with participation costs in the symmetric independent private values setting, where bidders know their valuations when they make independent participation decisions. After characterizing the optimal auction in terms of participation cut-o¤s, we provide an example where it is asymmetric. We then inves-tigate when the optimal auction will be symmetric/asymmetric and the nature of possible asymmetries. We also show that, under some conditions, the seller obtains her maximal pro\u85t in an (asymmetric) equilibrium of an anonymous second price auction. In general, the seller can also use non-anonymous auctions that resemble the ones that are actually observed in practice