Consider an auction in which the government wants to auction out a construction project, to the lowest bidding contractor. A group of bidders (firms) are attending theauction but none of the firms knows for sure how many other firms will participate in theauction. There will be either two or three other bidders in addition to your firm (total 3 or 4). All bidders have independent values (expected cost of the construction project to thefirm) for the contract, and if they can win the auction, their profit would be calculated as thecontract price (winning bid) minus the expected project cost (valuation of the firm). Yourfirm’s expected cost for the project is $C million dollars.

a. Assume that the government employs a sealed-bid first price auction, where theincremental bid is set as $1M and ties are broken using fair coin flip. If your firmbelieves that all other firms have the same expected costs (valuation) for the projectas your firm does ($C million), what bid should your firm submit, and how does it depend on the number of other bidders who attend the auction?

b. What are your firm’s expected profits from this auction, and how does it depend onthe number of other bidders who attend the auction?

c. Is the outcome of the sealed-bid first price auction Pareto efficient?

d. Now assume that the government instead holds a second-price sealed bid auction.Unlike in part a, your firm now believes that “Among all the participating firms, yourfirm has the unique lowest expected cost (valuation) for the project, $C. Further, thesecond lowest expected cost is $C/2+4 million, among the other firms”. What areyour firm’s expected profits in this auction?

e. Under what conditions (on “C”) is your firm happier (more expected profits) withsealed-bid first price auction scenario (parts a&b) vs. sealed-bid second priceauction scenario (part d), assuming there are 3 participating firms total.