Can you unlink game from old game centre account to new one?

[Michelle Stothard]

For some reason my game automatically linked to an old game centre account (which wasn't even signed in). How can I move my game onto my new game centre? Very frustrating as have friends wanting to join me in game but no one can find me! (My friends are all on my new gc). Also having to swap accounts to play all my other games. I log into new gc and it throws me back into the Dawn Age.