A Note on Auctions with Endogenous Participation

In this paper, we study an auction where bidders only know the number of potential applicants. After seeing their values for the object, bidders decide whether or not to enter the auction. Players may not want to enter the auction since they have to pay participation costs. We characterize the optimal bidding strategies for both first- and second- price sealed-bid auction when participation is endogenous. We show that only bidders with values greater than a certain cut-off point will bid in these auctions. In this context, both auctions generate the same expected revenue. We also show that, contrarily to the predictions of the fixed-$n$ literature, the seller's expected revenue may not increase when the number of potential participants increases. In addition, we show that it is optimal for the seller to charge an entry fee, which contrast greatly with results from the existing literature on auctions with entry.