The Game Center "Welcome back" banner not only slows down iOS games, but it has been known to disrupt game play. Unfortunately logging out of Game Center only replaces the banner with a sign in screen that can also interrupt game play and increase loading times. The only known way to disable the "Welcome back" banner is by installing the jailbreak tweak DisableWelcomeBanner. This tweak can be found for free on the kinchan repo at http://kindadev.com/apt/. You can read more about disabling Game Center here.
How can I disable the Game Center Welcome Back banner?
Taxonomy upgrade extras: