Repeat Exercise for the case in which there are two buyers, and their private values V1 and V2 are independent; V1 is uniformly distributed over [0, 2] and V2 is uniformly distributed over [0, 3].
Exercise
Suppose that there are n buyers whose private values are independent and uniformly distributed over [0, 1]. Answer the following questions:
(a) What is the individually rational, incentive-compatible direct selling mechanism that maximizes the seller's expected revenue?
(b) In this mechanism, what is each buyer's probability of winning the object, assuming that each buyer reports his true private value?
(c) What is the seller's expected revenue in this case?