A very old thread, but I've had a similar issue just now. The problem seems to be that I had my sandbox testing account signed in to the device. After signing it out, and signing back in to a Game Center account, the issue resolved itself.
Sharing for anyone who may have googled the error codes.
_authenticateUsingAlert:Failed to authenticate player with existing credentials.Error: Error Domain=GKErrorDomain Code=6
Noice2D
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