Auctions with endogenous participation

Abstract

We study endogenous-participation auctions where bidders only know the number of potential participants. After seeing their values for the object, potential participants decide whether or not to enter the auction. They may not want to enter the auction since they have to pay participation costs. We characterize equilibrium bidding strategies and entry decisions for both first- and second-price sealed-bid auctions when participation is endogenous. We show that there is a pure strategy entry equilibrium where only bidders with values greater than a certain cut-off point actually bid. In this context, both types of auctions generate the same expected revenue. We also show that, contrary to the predictions of the fixed number of bidders literature, the seller's expected revenue may decrease when the number of potential participants increases. In addition, we show that it is optimal for the seller to charge an entry fee, which contrasts with results from the existing literature on auctions with entry. As in the fixed-n literature, we show that first-price auctions generate more expected revenue than second-price auctions when buyers are risk-averse. Finally, we characterize the optimal auction -the auction that maximizes the seller's expected revenue -by using a direct revelation mechanism. The optimal auction involves a reserve price larger than the optimal reserve price in the fixed-n literature. The winner's payment is the second highest bid less the participation cost and losers receive a subsidy equal to the participation cost.