Once per game per player versus once per game for the group is pretty obvious.

But can multiple players trigger an ally once per round/phase each? The only relevant card for that would be Blue Mountain Trader.

And what about events? Is there a different ruling for limit once per phase/round? Traffic from Dale can be played by multiple players each round (one each), but it has different wording.

A quick look through Hall of Beorn doesn't show any once per round events that are ambigious. The only once per phase I saw was Heavy Stroke, I'd guess this is for all players since it doesn't specify, though once per enemy might be a more appropriate.

For Blue Mountain Trader I would interpret the once per round ability as once per Trader.

Thanks, do you know if a single player can play multiple (different) copies of a once per round event each round?

Usually restrictions like once per round are checked by card, this is the case for Blue Mountain Trader.

For events obviously this doesn't make sense since you can't play the same event twice (well, you can, but since it leaves play in the interim the game treats it as a new copy). So I believe any events with a once per phase restriction (I don't think there are any once per round events are there?) should be treated as if they have the more accurate later phrasing " [You/The players, as a group,] can only play 1 copy of [event] each phase."

Thanks.