THIS QUESTION IS ABOUT GAME THEORY.

Consider the first price sealed bid auction with two players where each player's value uniformly (and in-dependently) distributed over [0,1]. If a player whose value is v wins the auction by bidding b, her payoff is (vb)^1/2. Find a Bayesian equilibrium of this game in which each player uses the same bidding strategy i(v)=av, i = 1,2, where a>0.