Law enforcement sources tell us the guy who got into it with the rapper during the hoops game over the weekend is a rookie cop ... who was off-duty at the time.
It's interesting -- as TMZ first reported ... Game is saying the guy threatened him before the fight by hinting he was going to get a gun out of his gym bag. For his part, the punchee told responding officers Game is the one who issued a death threat. Our Game sources say he denies that.
We're told LAPD is investigating the Game for battery -- and also the off-duty officer. If he really did threaten to get his gun ... he could be in big trouble.