The U.S. Department of the Interior has announced its intention to use a sealed-bid, first-price auction to sell petroleum-drilling rights on public land in Alaska. Four oil companies have indicated their intention to participate in this auction. The problem is that the actual value of the oil reserves is unknown with certainty. Before submitting their bids, each oil company conducted independent seismic and geological tests to obtain an estimate of the quality and quantity of the petroleum reserves. The petroleum-deposit value estimates in millions of dollars of the four companies are V1 = $250, V2 = $170, V3 = $320 and V4 = $265. Although the companies do not know their rivals’ estimates, they believe that these valuations are independent and randomly distributed between a low value of L = $100 and a high possible price of H = $400.

a. What is the optimal bid of each oil company?

b. Who will win the auction and what price will the winner pay for the drilling rights?

c. Do you believe that the winner of this auction paid too much for the drilling rights? Why?