Hockey Fighting

Because this year the Buffalo Sabres picked up two new players who are built for wrecking people and getting in fights, I have learned a lot about fights and how they work. When hockey players get into a fight on the ice as they often do, there is a lot of physics involved. What usually happens when 2 players get in a fight, they grab each others jerseys with one arm and punch at each other with the other hand, and because when one person punches the other and the fist applies the same amount of force on the head as the head applies to the fist, they should hypothetically speaking stay still if they just stood there and punched each other because they are both applying a force exactly same to each other and they are holding on to each other while they do it.