Consider a sealed-bid auction in which the bidder with the highest bid wins the item and each bidder pays the average of the two highest bids; i.e., if the two highest bids were 0.9 and 0.8, then the winning bidder would pay 0.85.

Use the revenue equivalence theorem to derive the symmetric equilibrium bidding function b(v). As usual, assume that there are N bidders with private valuations v drawn independently from the uniform (0,1) probability distribution. Show your work.