This is not intentionally supported by Apple.
If you are writing this for an application that doesn't have to be distributed through the App Store, you can set the application up to play a silent audio file in the background. This will allow GameKit to continue to work even when your application has been put into the background or if the screen has locked.
If this application has to be distributed through the App Store, Apple require the audio to be a real feature, with audible music playing.
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