How to stop Game Center sign in prompts

Is there a way to stop the incessant Game Center Sign In prompts? Ever since the last iOS update, when ever I'm in an Arcade game the Game Center Sign In prompt pops up over and over and over and over again. I've signed out of Game Center, I've turned off Game Center notifications. What more do I have to do for Apple to get that I don't want to sign in to Game Center? Ever! If Apple thinks that relentless prompts will somehow get me to want to sign in, after I've made it clear that I don't, then they need to do their research, because it actually makes me want to figure out how to delete it entirely.