2. A seller uses a second-price sealed-bid auction to sell a painting to two bidders. The seller claims that the painting was drawn by a famous painter, say Monet. Both bidders are not sure about the seller's claim, and think that the probability of the painting being drawn by Monet is 1 / 2. Both bidders can examine the painting before bidding. After examination, bidder 1 gets signal :13] and bidder 2 gets signal 3:2. Both $1 and :52 are independently drawn from a uniform distribution on [0, 1]. Let us assume that if a bidder is an expert on Monet's painting, then after examination he or she can immediately know whether the painting is authentic. Otherwise, he or she still thinks that the probability of the painting being authentic is 1/2. If the painting is authentic, it will worth 10 + :31 to bidder 1, and will worth 10 +332 to bidder 2. If the painting is fake, it will worth $1 to bidder 1, and will worth 9:2 to bidder 2. Suppose you are bidder 1 and 331 = 0.6. (a) First suppose both you and bidder 2 know that neither you nor bidder 2 is an expert of Monet's painting. How much will you bid? Briey explain your answer. (b) Next suppose both you and bidder 2 know that bidder 2 is an expert while you are not. How much would bidder 2 bid? How much will you bid? Briey explain your answer. (C) Finally suppose you know that neither you nor bidder 2 is an expert. But bidder 2 is not sure whether you are an expert or not. Suppose you could pretend to be an expert and convince him that you are an expert. Will you choose to do so? Why? [hintz use (a) and (b)]