On the other hand, sometimes the kids enjoy hitting each other. This is very different from hitting out of anger: they're both having fun, they're not trying to injure each other, it's more about force than impact, etc. Even calling both of these activities "hitting" is a bit misleading: a hit intended to inflict pain looks very different than one intended to knock the other off balance or push them farther away on the couch to gain a strategic advantage.

We wouldn't want to prohibit our kids from playing roughly with each other when that's what they both want, but this interacts awkwardly with normal rules. If Lily says "Anna hit me" but this was after Lily said "Anna, lets play a game where we hit each other" then Anna should clearly not go in time out. The way we generally handle this is flagging to the kids when we notice they're doing this ("it looks like you're playing a rough game") and possibly including a warning ("and someone might get hurt"). Then if someone does get hurt, and minor injuries are reasonably common with this sort of play, they know we're not going to punish the other person for it ("you were playing a rough game, and this is the kind of thing that can happen when you're playing rough"). If they were doing this upstairs or somewhere we didn't notice we do our best to figure out what happened ("What were you doing before they hit you? ... It sounds like you were playing a rough game.") but it's not perfect.

One way this could be abused is to use the context of a rough game to escalate to actually trying to hurt the other person. How this works out sounds like something that would vary a lot based on the actual kids involved, but with ours this is rare: I don't see them using rough games as cover for malice. Much more common are issues with not being on the same page about whether they're playing a rough game. We sort that out as best as we can ("Anna, is this a game you want to be playing?") and try to encourage them to do this on their own ("Does it look like Lily's enjoying this?").

I'm also curious how this will change as our youngest (3y) gets into a range where she'll start being able to do this kind of play with her older siblings. She's a lot more fragile than they are, and much weaker, but this might be something where a larger difference in the ability to inflict harm makes it clearer whether actions are in the "rough game" category?

(Julia also touched on this in her "advice for getting along with your kids" post.)