Practically every member of Game Center can challenge you, whether it’s your friend or a stranger.
All challenges are visible under the “Challenges” tab of Game Center. If you don’t want to accept the challenge for whatever reason, simply click on the person that sent you challenge and click on the “Decline” button.
How to Challenge someone in Game Center
If you want to challenge someone, it’s quite simple.
To challenge your friends go to the “Friends” tab of Game Center, select a friend that you want to challenge to see which games you have in common with him, and select one of these games. After this, go to leaderboards, select a desired friend and click on the “Send Challenge” button.
NOTE: You can challenge strangers as well, but you will first have to add them as friends.
When you click on the achievements tab, you will be able to see a list of achievements awarded to you and your Game Center friends.
In this section you can challenge your friend to gain a certain achievement in the game. This can either be an achievement that you already have, or an unearned achievement – this can be very fun, since you can compete with your friend, on who will get that achievement first.
Your friends can view the challenges you sent in their Game Center account under the “Challenges” tab.