How about defining land as public property, as opposed to not defining land as no property at all? 'Cause the latter seems rather unfeasable; we might all want to live in the heart of London or Paris or whatever.
http://en.wikipedia.org/wiki/Tragedy_of_the_commonsSorry, I think I'm missing your point?
How are we gonna decide who gets to live on the Champs-Élysées? What has the Tragedy of the Commons got to do with this?
My point: If all land is held "in common," the people who use that land have less care for it. Think about it: Would you throw a Styrofoam cup onto your front lawn? Yet, many people litter while driving down the road.
As to your other two questions:
Yes, we can't all live on the Champs-Élysées (even if all land is held in "common"). That's why, to prevent conflict, we recognize two ways of acquiring land:
Original appropriation, and voluntary sale. That way, land goes to those who value it most.