You are a bidder in an independent private values auction, and you value the object at $4,500. Each bidder perceives that valuations are uniformly distributed between $1,500 and $9,000. Determine your optimal bidding strategy in a first-price, sealed-bid auction when the total number of bidders (including you) is:

a. 2 bidders. Bid: $

b. 10 bidders. Bid: $

c. 100 bidders. Bid: $