32. Consider the Vickrey auction for a lamp that is worth $100 to our bidder Bob (page 559). Suppose someone suggests that Bob would always do as well with a bid of $80. Show that this is false by playing the role of another bidder who could make Bob regret a choice of bidding $80 rather than his (sincere) bid of $100. You are free to make any assumptions that you want about the bids other than Bob’s and your own.