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 x1 and bidder 2 gets signal x2. Both x1 and x2 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+x1 to bidder 1, and will worth 10+x2 to bidder 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?