Someone at a party pulls out a $100 bill and announces that he is going to auction it off. There are n ≥ 2 other 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. Everyone (not just the highest bidder) pays his bid, and the bidder with the highest bid gets the $100 bill (assuming that the highest bid is positive). If m people submit the highest bid, then each receives a share of the $100. Each person’s strategy set is so bidding can go as high as $1,000. If denotes the bid of player j and is the maximum (or highest) of the n bids, then the payoff to player i is
where m is the number of bidders whose bid equals Find all Nash equilibria.