Hi, this has to do with auctions and mechanism design!

In a first-price, all-pay auction, the bidders simultaneously submit sealedbids. The highest bid wins the object and every bidder pays the seller the

amount of his bid. Consider the independent private value model with symmetric bidders whose values are each distributed according to C.D.F.

F with p.d.f. f

What I'm stuck on and need help figuring out is

1) the unique symmetric equilibrium bidding function

2) an expression for the seller's expected revenue

3) showing that the seller's expected revenue is the same as in the first price auction, both using the revenue equivalence theorem and without using it

Thank you so much for any help you can give!