According to the Federal Communications Commission, gaming consoles that require an internet connection, like Fortnite, usually need a bandwidth of 3Mbps. And online multiplayer games, like Call of Duty, need a bandwidth of 4Mbps.
The short answer is this: you only need about 5 to 10 Mbps minimum for most online games, even new AAA titles like Call of Duty: Modern Warfare II. But we recommend that you have at least 50 to 100 Mbps if you're really trying to grind in your favorite games, whether on PC or console.