A town wants to build a new bridge. Construction firms will submit sealed bids

The town will award the contract to the firm that submits the lowest bid and will pay the firm the amount of the second lowest bid (that is, the town will conduct a second-price procurement auction). So, for example, if Firm A bids $8 million, Firm B bids $9 million, and Firm C bids $10 million then the city will award the contract to Firm A (it submitted the lowest bid) and pay Firm A $9 million (the amount of the second lowest bid). Suppose your firm is willing to build the bridge for a minimum of $9 million. a. Show that bidding $9 million is a better strategy than bidding some amount below $9 million— say, $7 million. b. Show that bidding $9 million is a better strategy than bidding some amount above $9 million—say, $11 million.

a. Suppose you bid $7 million. If another firm bids less than $7 million, you will not win the contract whether you bid $9 million or $7 million. If another firm bids something between $7 million and $9 million you will win the contract but you will suffer a loss (since you will be paid less than $9 million). If the lowest bid other than yours is above $9 million you will win and will be paid more than $9 million; this is exactly what would have happened if you had bid $9 million. So you cannot gain by bidding less than $9 million but you could lose.
b. Suppose you bid $11 million. If another firms bids less than $9 million you will not win the contract. Again, this is the same outcome had you bid $9 million. If another firm bids something between $9 million and $11 million you will again lose the contract. If you had bid $9 million you would have won and would have earned a profit (since you would have been paid more than $9 million). If the lowest bid other than yours is above $11 million you will win and will be paid more than $9 million; this is exactly what would have happened if you had bid $9 million. So you cannot gain by bidding more than $9 million but you could lose the chance to earn a profit.