Suppose you and one other bidder are competing in a private-value auction. The auction format is sealed bid, first price. Let v and b denote your valuation and bid, respectively, and let 
n and bn denote the valuation and bid of your opponent.
Your payoff is - b if it is the case that b ≥ bn. Your payoff is 0 otherwise. Although you do not observe n, you know that vn is uniformly distributed over the interval between 0 and 1. That is, is the probability that n 
.
You also know that your opponent bids according to the function bn(vn) = vn2 . Suppose your value is 3/5. What is your optimal bid?