This is might be useful if you’re a parent concerned with your child’s safety online, or you just don’t want to deal with anyone else!
In involves the ‘Restrictions’ feature in Settings
Settings > General > Restrictions (scroll right to the bottom to get to it)
Then disable ‘Multiplayer Games’ and ‘Adding Friends’
This also sometimes fixes bugs that involve interruptions by a Game Center ‘alert’. These are alert that comes up onscreen in Game Center or right in the middle of a game you’re playing – they’re native to Game Center and are not the same as standard iOS notifications.
You can also use Game Centre on the Mac.