Entry in the Second-Price Auction

There are TWO bidders who have independent private values, v1 and v2. For Bidder 1, his value can be either $10 or $40, each with probability of 1/2. For Bidder 2, her value can be either $20 or $50, each with probability of 1/2. These value distributions are common knowledge. Standard rules of the second-price auction apply. There is no reserve price in this auction.

(a) For each bidder, calculate its expected payoff (before the bidder learns its value) in this auction.

For the rest of the question, suppose that each bidder has to pay $6 to an intermediary to submit the bid in this auction (i.e., a cost of participation). If a bidder decides to participate, a bidder has to pay $6 before learning its own value. A bidder can always decide not to participate in the auction and avoid spending $6.

(b) Calculate the auctioneer's expected revenue in this auction. (Hint: You need your answers for part (a) here)

(c) Now suppose that the auctioneer can choose to subsidize the cost of intermediary by reimbursing $6 to each bidder who submitted a bid. Calculate the auctioneer's expected revenue in this auction (accounting for the cost of reimbursement) and argue whether or not the auctioneer should implement this subsidy.