Repeat Exercise when the cumulative distribution function of each buyer i's private value is Fi(v) = v3.
Exercise
Consider a symmetric sealed-bid first-price auction with independent private values with n buyers whose cumulative distribution function F is given by F(v) = v2.
Find the symmetric equilibrium, compute ei(vi) (the expected payment of buyer i if his private value is vi), compute ei (the payment that buyer i makes), and compute π (the seller's expected revenue).