Probably too late to help, but I just had a same error on my macOS recently.
Turns out I just needed to sign out of iCloud and sign in again in the system. When I signed back in (with the same account), I needed to accept new terms of service so maybe it was stuck on that.
martin243
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Make sure you have "com.apple.security.network.server" and "com.apple.security.network.client" entitlements in case you have the sandbox on:
https://stackoverflow.com/questions/27728072/game-center-matchmaking-on-os-x-yosemite-not-working
That helped me to be able to send the invites at least. Receiving invites may be a different issue.