Need help with this game theory question

4. Consider the all-pay privatevalue auction where there are n. = 2 bidders, each with a value drawn independently from a distribution F on [0,3]. Assume that F has a derivative that is given by the function f (the density function of the distribution}. If player j follows a symmetric bidding strategy Hwy}, the expected utility of a bid 5,- by player i is given by: Pl'{.3_1[5i}2 \"5} w.- - be the probability 13's bid is the highest multiplied by the value of the object minus the bid, which is paid for certain (that is why this auction format is called 'allpay'). (a) Find the bestresponse bid {1* for bidder i when their value is w; and the other player bids according to the bidding function ,3. Assume that ,1? is an invertible flmction. [b] 1What is the condition for w'} to be a symmetric Bayesian Nash Equilibrium of this game? (c) Find the symmetric equilibrium bid function when the distribution function is given by: L a uniform on [Chm so that the value GDP is F.4(Il- = Pr{a: 2 mg} = 2 iii A linear increasing density+ so that the value GDP is ngm) = i2 a: EIIH (d) Draw on the same graph the two allpay bid functions under the two value distributions FA and F3