Q2 Revenue equivalence I

Consider a sealed-bid auction in which the seller draws one of the N bids at random. The buyer whose bid was drawn wins the auction and pays the amount bid. Assume that buyer valuations follow a uniform(0,1) distribution.

1. What is the symmetric equilibrium bidding strategy b(v)? Explain in words why you know this

2. What is the seller's expected revenue?

3. Why doesn't this auction pay the seller the same revenue as the four standard auctions? That is, why doesn't the revenue equivalence theorem apply here? Be specific.