Pay-to-bid auctions: To bid or not to bid

We propose an all-pay auction format with risk-loving bidders paying a constant fee each time they bid for an object whose monetary value is common knowledge among the bidders, and bidding fees are the only source of benefit for the seller. We characterize a unique symmetric sub-game perfect equilibrium, and further show that the expected revenue of the seller is independent of the number of bidders, decreasing in the sale price and bidding fee, and increasing in the value of the object.