In an all-pay auction, all the bidders must actually pay their bids to the seller, but only the high bidder gets the object up for sale.
This type of auction is also called a charity auction. By following the procedure for a Dutch auction, show that the equilibrium bidding function for all players is β(v) = ((N − 1)/N)v N, assuming that bidders’ valuations are uniformly distributed on the normalized interval [0, 1]. Find the expected total amount collected by the seller.
In an all-pay auction, all the bidders must actually pay their bids to the seller, but only the high bidder gets the object up for sale.