Consider the simple private-value auction with 6 bidders. Each bidder's value is drawn independently from U[4,10].

(a) Suppose that the seller holds a second-price auction. What is the expected payo of a bidder with value v [4,10]?

(b) Suppose that the seller holds an auction with the following rules: the highest bidder wins the auction and pays the square of her bid (e.g., if bids are $6, $5, $4, $3, $2, $1, the payment is $36). Find an equilibrium bidding strategy.