Game Theory

2. A stamp collector is considering selling one of her prize stamps.Based on some very insightful market research, she knows that there are two bidders, and each bidder just wants to add the stamp to their own private collection and is not worried about resale value.Depending on their mood the day of the auction, each bidder is equally likely to value the stamp at $10, $20 or $30.(The realized values are not correlated across the two bidders, i.e. they are independent, private values.Also assume everyone, including the seller, is risk neutral, and if there is a tie, we can flip a coin to determine the winner.)

a. If the stamp collector values the stamp at $11, what is her expected profit from using a sealed-bid second-price auction?

b. Suppose the stamp collector decided to run a first-price sealed-bid auction, rather than a second-price sealed-bid auction.Why might the bidders be more comfortable with a first-price auction, especially if they can't verify the seller is honest?