Prove the revenue equivalence theorem between second$-$price auction and all$-$

payauctionfor N bidderswithi.i$.$d$.$ uniformdistribution v i $$Uniform$[0,1]$onsingleitem$.$ In

all$-$pay auction, each bidder pay his$/$her bid, regardless of whether being allocated, and the

bidder with the highest bid is allocated the item