You are one of five risk- neutral bidders participating in an independent private values auction. Each bidder perceives that all other bidders’ valuations for the item are evenly distributed between $ 10,000 and $ 30,000. For each of the following auction types, determine your optimal bidding strategy if you value the item at $ 22,000.

a. First- price, sealed- bid auction.

b. Dutch auction.

c. Second- price, sealed- bid auction.

d. English auction.