Suppose you are a network systems provider and are bidding for the job of providing and installing a system for a new government office building. You are considering submitting one of three bids: a low bid of $500,000, a medium bid of $600,000, and a high bid of $700,000. The cost of the job to you will be $450,000, regardless of your bid. Thus, if you submit a bid of $500,000 and win the contract, your profit will be $500,000 − $450,000 = $50,000. If you win with a bid of $600,000, your profit will be $150,000. If you do not win the contract, your profit will be zero. Two competitors will also submit bids. Each competitor will bid $500,000, $600,000, or $700,000 with probability 1/3 each, with your competitors' bids being independent of each other. The contract will be awarded to the lowest bidder. In the case of a tie, the contract will be awarded to the bidder with the most experience. In this case, you will certainly win because your company has more experience than the other two. The bids are sealed and made simultaneously.

(a) If you bid medium ($600,000), what is your probability of winning the contract?
(b) Draw a decision tree to determine which bid (low, medium, high) yields the highest expected profit for you.
(c) Suppose a clairvoyant could tell you in advance exactly what both competitors’ bids will be. What is the expected value of this information? (d) Suppose instead that the clairvoyant could tell you in advance exactly what competitor #1's bid will be, but you would remain uncertain about competitor #2's bid. What is the expected value of this information?