1. The deduction leading to equation (3.1) is incomplete as b1 may not be in the range of b(·). Reduce the general case to the case b1 ∈ b([0, 1]).
2. Compute the seller's expected revenue if the number of bidders goes to infinity.
3. In the text we assumed that in case of a tie the object is not delivered to any bidder. Show that the equilibrium strategies obtained above (for both first- and second-price auctions) still hold under any tie-breaking rule.