Beginning iOS Game Center and Game Kit: For iPhone, iPad, and iPod touch

Handling Incoming Invitations

When implementing matchmaking into your app, you also have to implement a system to handle invitations from friends. The invitee's device will receive a push notification informing them that one of their friends has invited them to play a game. Assuming they have the game installed and accept the invitation, you will be required to handle connecting the two players together via a new match. If the invitee does not have the game or app installed, they will be instructed to download it. After the download is finished, the normal invitation process is followed.

NOTE: You will also need to process invitations from new matches created within Game Center.app. You most likely won't need to write any additional code; however, ...