Epic and Steam offer free peer-to-peer connections for games hosted on itch.io games? I know Steam gives developers access to their APIs for free, but I thought it had to be a steam game and the user needs to be logged in to steam. How does that work?
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Yeah you're right about Steam, its P2P goes through the Steam client so everyone does need Steam open and logged in, no way around that. And you do need an App ID, most people just use Spacewar (480) for testing but you'd want your own to actually ship if you plan on a proper release.
EOS is the exception, one of its policies lets players log in anonymously with a device id so there's no account or client they need running.
They made that for crossplatform compatibility.
Worth mentioning all of this is for downloadable builds by the way, if it's a browser game on itch none of it applies, that's a whole different setup (WebRTC/websockets stuff).