The Internal Revenue Service has organized a sealed-bid auction to sell an office building whose owners have failed to pay back taxes.
a. As a real-estate developer, you estimate the value of the building to be $2.9 million. You believe that a typical competitor’s bid will be in the range of $2 million to $3 million (with all values in between equally likely) and that bids are independent of one another. You are considering bids of $2.4 million, $2.6 million, and $2.7 million. Which bid provides the greatest expected profit against one other bidder? Against two other bidders?
b. Now suppose that you face two other bidders and believe that a typical competitor’s value for the building lies between $2 million and $3.5 million, with all values in between equally likely. (Again, your value is $2.9 million.) Assuming your two rivals employ equilibrium bid strategies, what is your equilibrium bid?