Someone at a party pulls out a $100 dollar bill and announces that he is going to auction it off, and 20 other people at the party are potential bidders. The owner of the $100 bill has the following rules: All bidders must simultaneously submit the written bid. Everyone pays their bid, not just the highest bidder. The bidder with the highest bid gets the $100 bill. If m people submit the highest bid, then each recieves a l/m share of the $100.

Each persons strategy set is (1,2,3......1000) as bidding can go as high as $1000. If Bi denotes the bid of player i, then playes i's payoff is

-Bi if Bi is not the highest bid

100/m - Bi if Bi is the highest bid

where m denotes the number of people who submitted the highest bid including player i.

Find all Nash Equilibriu,