  We propose a new all-pay auction format in which risk-loving bidders pay 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 show that for the proposed model there exists a {unique}
Symmetric Subgame Perfect Equilibrium (SSPE). The characterized SSPE is
stationary when re-entry in the auction is allowed, and it is Markov perfect
when re-entry is forbidden. Furthermore, we fully characterize the expected
revenue of the seller. Generally, with or without re-entry, it is more
beneficial for the seller to choose $v$ (value of the object), $s$ (sale
price), and $c$ (bidding fee) such that $\frac{v-s}{c}$ becomes sufficiently
large. In particular, when re-entry is permitted: the expected revenue of the
seller is \emph{independent} of the number of bidders, decreasing in the sale
price, increasing in the value of the object, and decreasing in the bidding
fee; Moreover, the seller's revenue is equal to the value of the object when
players are risk neutral, and it is strictly greater than the value of the
object when bidders are risk-loving. We further show that allowing re-entry can
be important in practice. Because, if the seller were to run such an auction
without allowing re-entry, the auction would last a long time, and for almost
all of its duration have only two remaining players. Thus, the seller's revenue
relies on those two players being willing to participate, without any breaks,
in an auction that might last for thousands of rounds
