Assume that there are n bidders participating in a First Price Auction. Each bid- der's private valuation is independently drawn from the interval [0, 1] according to the distribution with cdf F(x) = x2 and pdf f(x) = 2x.
1. Explain the bidder i's expected profit function and you may assume that all of the other bidders bid a fraction of their valuations: bj = θvj.
2. Identify the profit-maximizing condition for bidder i's bid by taking the derivative of this profit function you defined in part (a) and setting this equation equal to zero.
3. Determine the symmetric Bayesian Nash equilibrium in this auction?