Please solve this question

07. Consider the following first-price sealed-bid auction where an indivisible good is sold. There are n 2 2 buyers indexed by i = 1, 2,3,..., n. Simultaneously, each buyer { submits a bid by 2 0. The agent who submits the highest bid wins. If there are k > 1 players submitting the highest bid, then the winner is determined randomly among these players - each has probability 1/k of winning. The winner i gets the object and pays his bid by, obtaining payoff (vi - b;), while the other buyers get 0, where v1, ...., Un are independently and identically distributed with probability density function f where f ( x ) = 13x2 x E [0,1] otherwise. (a) Compute the symmetric, linear bidding strategy in a Bayesian Nash equilibrium. (b) What happens as n - co? (c) What would be the expected payment of a bidder with a given value x and finite n 2 2? (d) What would be the ex-ante expected payment of a bidder (for finite n)