Another animator's model, however, is a different story. That's where we start using a dirty word: cooperation.

Yes, even though your characters are doing their level best to dash each other's brains out on the nearest available surface, the two animators are going to have to cooperate very closely.

Obviously, each pair (or triple, or whatever) of animators who have their characters face off will make up their own methods for making sure the animation gets done. It's just like any other collaborative project, really. However, in the interest of starting everyone off, here's a recommended way to get the first couple of dozen frames turned out:

First, one animator will animate their character's attack. That animator will also animate the response of the opposing character. They will send both of these action files to their counterpart animator.

Second, the counterpart animator (i.e. the one whose model has just been punched) should feel free to modify the animation they were handed so far. They can change how their character reacted. They can also change how the attacking character's movement differed due to that changed reaction.

Third, the animators now trade places. The animator whose model was defending is now free to go on the offensive, and again, may animate the effects their models' blows have on the target model. They would then send the actions over to their partner, and the whole cycle would continue.