a) Suppose Alice runs a first-price auction. What would you advise Bob to bid? Why?

b) Suppose Alice runs a second-price auction. What would you advise Bob to bid? Why?

c)Suppose Alice runs a third-price auction. What would you advise Bob to bid? Why?

2. Alice is selling two identical watches by auction. There are three bid- ders, Bob, Charlie and Daphne, and each will buy at most one watch. Bidders' values are independent and private. Bidders always have the option not to participate, which is the same thing as bidding $0. Bob's value for the watch is $400. He doesn't know what the other bidders will do, but his best guess is that Charlie's bid will be uniformly distributed on the interval [0,500] and Daphne's 0n the interval [500,1000]. (a) Suppose Alice runs a rstprice auction: All three bidders submit bids simultaneously, and the top two bidders each pay the highest bid and receive a watch. What would you advise Bob to bid? Why? (b) Suppose Alice runs a second-price auction: All three bidders sub- mit bids simultaneously, and the top two bidders each pay the second-highest bid and receive a watch. What would you advise Bob to bid? Why? (c) Suppose Alice runs a third-price auction: All three bidders submit bids simultaneously, and the top two bidders each pay the third- highest bid and receive a watch. What would you advise Bob to bid? Why