I don't think Uber necessarily needs a monopoly to win, if Lyft wants to compete on price it's free to due so, but if Uber has thin margins as it is, undercutting them is just a shortcut to death.
I might be unreasonably optimistic about self-driving cars, but it is important to note that the rollout will accelerate itself. The more SDCs on the road, the safer they'll be, and the more data they'll gather. On the legislation side, my sense is that once one company bears the brunt of the legal pushback, the rest will have a relatively easy time.
Not that BI has a crystal ball, but their prediction seems at least somewhat reasonable. [1]
[1] http://www.businessinsider.com/report-10-million-self-drivin...