Solve please

(10 pts) Two bidders participate in an all-pay common-value auction for an oil tract. Bidder 2' privately observes a signal 51-. The signals 51 and 52 are uniformly and independently distributed on [0,1]. The value 6 of the oil tract to whoever wins it is determined by the signals: 1 If bidder 2? bids b and wins (i.e., b is larger than the other bidder's bid), her payoff is 1'3 b. If she loses her payoff is b. There is a strictly increasing differentiable bid function b : [0, 1] > IR such that it is an equilibrium for each bidder i to bid b(.31-) when her signal is [3} = 31-. Derive this bid function