一道博弈论auction的题，有人会吗，万分感谢！

3. Consider a sealed-bid second-price auction with two buyers, whose private values are independent; V1 ～ U[0, 1] while V2 ～ U[0, 2]. 

a. Find a weakly dominating strategy for each player. ( 1 15 total mark) 

b. Consider the equilibrium in which buyer bid their valuation. What is the probability that buyer 1 wins the item? What is the sellers expected revenue in this case? ( 3 30 total mark) 

c. Prove that if β = (β1, β2) is an equilibrium in which β1(v) = β2(v) for every v ∈ [0, 1] then β1(v) = β2(v) = v for every v ∈ [0, 1]. ( 3 30 total mark) 

d. Is there an equilibrium in which a buyer with valuation < 1 does not bid her valuation? ( 1 15 total mark)