Consider a government running a procurement auction in which bidders bid their costs. The bidder with the lowest bid wins the auction and receives its own bid. If there are multiple lowest bids, then one of them is randomly chosen with equal probability. Each bidder's payoff is zero if she loses, and the payoff is the bid minus the true cost if she wins. Suppose that the true cost is distributed uniformly between 0 and 200, independently across all the bidders. There is a unique equilibrium in the bidders' game. In the following questions, consider this unique equilibrium. 2 a. Suppose that there are 3 bidders. Suppose the true cost of Japan Construction (JC), a bidder, is 60. What is JC's bid? What is the probability of JC's winning? b. Suppose that one more bidder joins the auction. Does the probability of JC winning increase or decrease? Does the expected payment from the government increase or decrease? c. Provide an auction rule that is not strategically equivalent but is revenue equivalent to the given auction rule