I tried adding GameCenter to a prexisting app that I made, and when I turned GameCenter on in the capabilites section of XCode, it gave me an error saying "Add the GameCenter entitlement to your App ID, and below that, it says "An App ID with identifier (app id of my app) is not available. Please enter a different string." However, in the past, I have not had issues with the app ID, and in the past, I tried submitting the app to the app store. I looked online and couldn't find anything that worked for me. I am using XCode 7.3 with OSX 10.11.4.
App ID with identifier is not available
Did you ever figure it out?