The Game -- Allegedly Attacks Another Guy Connected to Basketball Brawl

The Game allegedly attacked a photog who was part of a team serving him with a lawsuit for allegedly assaulting a cop ... lots of allegeds here.

TMZ broke the story ... Game got into it with an off duty cop during a basketball game last month and sucker punched the guy. The cop has sued game, claiming the punch may have caused brain damage.

But lawsuits must get served, so Saturday afternoon a process server went to Game's Calabasas home to get the job done. He brought along a guy to record the service on video.

Apparently Game didn't much like the spotlight, because the photog says the rapper attacked him, pushing him to the ground.

The guy called 911, cops rushed over but by that time Game was gone. So the photog filed a police report for battery.