Suppose there are just two bidders. In a second-price, all-pay auction, the two bidders simultaneously submit sealed bids. The highest bid wins the object and both bidders pay the second-highest bid.
(a) Find the unique symmetric equilibrium bidding function. Interpret.
(b) Do bidders bid higher or lower than in a first-price, all-pay auction?
(c) Find an expression for the seller’s expected revenue.
(d) Both with and without using the revenue equivalence theorem, show that the seller’s expected revenue is the same as in a first-price auction.