Someone at a party pulls out a $100 bill and announces that he is going to auction it off. There are n = 10n=10 people at the party who are potential bidders. The owner of the $100 bill puts forth the following procedure: All bidders simultaneously submit a written bid. Only the highest bidders pay their bid (assuming that the highest bid is positive). If mm people submit the highest bid, then each receives 1/m1/m of the $100. Each person’s strategy set is {0, 1, 2, . . . , 1000}{0,1,2,...,1000} so bidding can go as high as $1,000

How many pure-strategy Nash equilibria does this game have?