It sounds like you want to check out Leaderboards https://developers.google.com/games/services/common/concepts/leaderboards
You can create (currently) up to 70 leaderboards (maybe one for the
country/regions of your players).
At the end of your game, you can update the user's score. The server
keeps track of daily, weekly, and all time leaders. There is also the
concept of Public and Social leaderboards so that may be a way to see the