Problem 2: As a Differ, you are holding a second-price allcool to select a seller. Qualities of sellers are identical, but you do not know their costs exactly. All you know is that each seller's cost has 1/3 of probability of being 150, 120, and 90 respectively. The cost distribution is independent between the sellers. It is possible that the lowest and the second lowest costs submitted by the sellers are the same. In this case, you will pay exactly that amount (for instance, if all sellers submit 150, then you select one seller at random and pay 150. If two or three sellers submit 90, then you select one of them in random and pay 90). Suppose that you now have two sellers participating in the auction. 1. What is expected value of your payment to the selected seller? 2. If it costs 20 to invite the third seller to participate in the auction, would you pay for it? Or should you just have an auction with two sellers