The clients determined their own position, yes. It was not a peer to peer game and the server ran sanity checks on what the client was telling it (is their velo

The clients determined their own position, yes. It was not a peer to peer game and the server ran sanity checks on what the client was telling it (is their velocity acceptable for the car they have? did they accelerate too fast? are they in an area of the world that should not be accessible? etc) which worked pretty well. We deemed it was too resource intensive and too slow to run a physics engine on the server (it was a "massively multiplayer" game).