I was wondering if this was a common behavior and what might be behind the
actions. Is it training, and if so for which bird the crow or the hawk? Or
was it just a game?

I often see it as a combination of training and playing.
I observed similar 'confrontations' recently between?three juvenile Sharp-shins, one juvenile Cooper's Hawk,?and several?Steller's Jays. They entertained me for the better part of three days and no one appeared to be harmed in the process.?

Joe Meche
Bellingham