In its release notes for iOS 10, Apple says that developers will now need to implement their own leaderboard interface using GameKit.
The Game Center app has been removed. If your game implements GameKit features, it must also implement the interface behavior necessary for the user to see these features. For example, if your game supports leaderboards, it could present a GKGameCenterViewController object or read the data directly from Game Center to implement a custom user interface.
Apple also made a few other changes to GameKit:
● A new account type, implemented by the GKCloudPlayer class, supports iCloud-only game accounts.
● Game Center provides a new generalized solution for managing persistent storage of data on Game Center. A game session (GKGameSession) has a list of players who are the session’s participants. Your game’s implementation defines when and how a participant stores or retrieves data from the server or exchanges data between players. Game sessions can often replace existing turn-based matches, real-time matches, and persistent save games, and also enable other models of interaction between participants.
As iOS 10 is still in its first beta, Apple could bring back Game Center; however, it seems unlikely as it's asking developers to build their own interfaces to GameKit features.
Another notable change in iOS 10 is the ability to delete stock apps. More details on that here.
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