Consider an auction with two bidders. The auctioneer believes that each of the f
ID: 1120947 • Letter: C
Question
Consider an auction with two bidders. The auctioneer believes that each of the following two cases occurs with probability 1/2. Case 1: Bidder A has a value for the object of $60, Bidder B’s value is $40. Case 2: Bidder A has a value of $80, Bidder B’s value is $20. Assuming the bidders follow the bidding strategies we derived in class, which of the following statements is true?
a. In this example, the auctioneer’s expected revenue is the same irrespective of whether he uses a first-price or second-price auction.
b. In this example, the auctioneer’s expected revenue is $30 in a first-price auction and $35 in a second-price auction.
c. In this example, the auctioneer’s expected revenue is $35 in a first-price auction and $30 in a second-price auction.
d. None of the above.
Explanation / Answer
Expected Revenue (ER) = Amount x Probability
Thus in case 1. the ER = 60x1/2 + 40x1/2 = 50
In case 2: the ER = 80x1/2 + 20x1/2 = 50.
Hence the expected revenue is same in both the cases.
Therefore, in this example, the auctioneer's expected revenue is the same irrespective of whether he uses a first price or second price auction. That is option (a) is correct.