Microeconomics

2. (20 points) Consider the two-bidder auction example in class, where bidder i's valuation, V,, is equal to 1 with probability q 6 (0,1) and 0 with probability 1 q, for z' = 1, 2. Assume V1 and V2 are mutually independent. The object is sold by a rst-price auction. The bidders are allowed to bid any nonnegative price. Whenever there is a tie, each bidder gets the good with probability 1/2. (a) Argue that, when V,- = 0, it is weakly dominant for player 2' to bid B,(0) = 0 for i = 1,2. (b) Show that there does not exist an equilibrium in which 31(1) = 32(1) = 3 /4. (c) Find the mixed strategy Nash equilibrium when q = 1/4. (d) Argue that the expected revenue of the seller in a rst-price auc- tion is lower than that in posted-price selling