Suppose there are n buyers participating in an auction, where the private values V1, V2,...,Vn are independent and identically distributed, with the cumulative distribution function
Fi(vi) = 1/2 vi + 1/2 (vi)2, vi ∈ [0,1].
Answer the following questions:
(a) Which auction maximizes the seller's expected revenue?
(b) What is the seller's expected revenue in this auction? (To answer this, it suffices to write the formula for the seller's expected revenue, and specify the values of the variables. There is no need to compute the formula explicitly.)
(c) Is the seller's expected revenue monotonically increasing as the number of buyers in the auction increases? Justify your answer.