A seller decides to sell an object by means of a sealed-bid, second-price auction without a reservation price.There are two bidders.The seller believes that for each of the two bidders there is a probability of 1/2 that the bidder's value for the object is $600 and a probability of 1/2 that the bidder's value is $300.The seller believes that these probabilities are independent between bidders.If the bidders bid rationally, what is the seller's expected revenue from the auction?
A)$360
B)$450
C)$375
D)$600
E)$420

Question

Quizplus · Accepted Answer

In a sealed-bid, second-price auction, the highest bidder wins the object but only pays the second-highest bid. Therefore, bidders have an incentive to bid their true value for the object. 
For each bidder, there is a 1/2 chance their value is $600 and a 1/2 chance their value is $300. The expected value of their bid is then: 
(1/2)($600) + (1/2)($300) = $450 
Therefore, the expected revenue for the seller is the sum of both expected bids, which is: 
$450 + $450 = $900 
However, since this is a second-price auction, the seller will only receive the second-highest bid. So, the expected revenue for the seller is actually: 
(1/2)($600) + (1/2)($300) = $375 
Thus, the correct answer is C) $375.

A Seller Decides to Sell an Object by Means of a Sealed-Bid