In this problem we will ask how the number of bidders in a second-price, sealed-bid auction affects how much the seller can expect to receive for his object. Assume that there are two bidders who have independent, private values vi which are either 1 or 3.

For each bidder, the probabilities of 1 and 3 are both 1/2. (If there is a tie at a bid of x for the highest bid the winner is selected at random from among the highest bidders and the price is x.)

(a) Show that the seller's expected revenue is 6/4.

(b) Now let's suppose that there are three bidders who have independent, private values vi which are either 1 or 3. For each bidder, the probabilities of 1 and 3 are both 1/2. What is the seller's expected revenue in this case?

(c) Briefly explain why changing the number of bidders affects the seller's expected revenue.