h

4. (20 points) (try this question after next week's lecture). A seller is selling one unit of an indivisible commodity through rst price sealed bid auction- There are 2 bidders indexed by 1' = 1,2. Simultaneously each bidder submits a sealed bid 5,- 2 U. The highest bidder wins and pays her bid. If bidder i is the winner, and her bid is b,- then her net payo is v,- bi. If bidder 2' does not win, she gets a payoff of 0. Each bidder i knows her value, 1),- for the object ( her maximal willingness to pay) but does not know the value of the other bidder of. It is commonly known that In , 1);; are distributed identically and independently over the interval [0, 1] according to the distribution function, F(:r) = :r In the symmetric equilibrium of this game nd the equilibrium bid function for a bidder