We study the optimal entry fee in a symmetric private value first-price auction with signaling, in which the participation decisions and the auction outcome are used by an outside observer to infer the bidders' types. We show that this auction has a unique fully separating equilibrium bidding function. When the bidders' sensibility for the signaling concern is sufficiently strong, the expected revenue maximizing entry fee is the maximal fee that guarantees full participation. The larger is the bidder’s sensibility, the higher is the optimal participation.
Bos, Oliver and Tom Truyts (2022), Entry in First-price Auctions with Signaling, International Journal of Game Theory