4. Suppose that there are three bidders with values that are drawn independently from U[1,3] in...

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4. Suppose that there are three bidders with values that are drawn independently from U[1,3] in an auction with one item. (a) Find an equilibrium of the second-price auction. Compute the expected value of the winning bidder and the expected revenue for the seller. (b) Find an equilibrium of the first-price auction. Compute the expected value of the winning bidder and the expected revenue for the seller. (Hint: You can assume that the equilibrium bidding function is of the form (v) = 1+ (v - 1), for some > 0. The reason that the intercept is 1 is that a bidder with the lowest possible value (that is, 1) will surely lose (since his opponent has a higher valuation with probability one) and must be willing to bid as high as his valuation.) 4. Suppose that there are three bidders with values that are drawn independently from U[1,3] in an auction with one item. (a) Find an equilibrium of the second-price auction. Compute the expected value of the winning bidder and the expected revenue for the seller. (b) Find an equilibrium of the first-price auction. Compute the expected value of the winning bidder and the expected revenue for the seller. (Hint: You can assume that the equilibrium bidding function is of the form (v) = 1+ (v - 1), for some > 0. The reason that the intercept is 1 is that a bidder with the lowest possible value (that is, 1) will surely lose (since his opponent has a higher valuation with probability one) and must be willing to bid as high as his valuation.)