Great question! The project would be built on the machine of the developer who initiated the Live Share session. That developer is effectively the "owner" of the session, and all developers who join the session are connecting their editor/IDE to theirs, and remoting certain editing/building/debugging operations. This allows the participants to fully collaborate, investigate/explore the project independently, but without incurring additional environment/setup requirements simply to get started.

We want the act of providing feedback/advice/etc. to each other to be as lightweight/frictionless as possible. Ideally, it would be so easy to collaborate, that it becomes harder for teams _not_ to do it :)