So long as Uber is selling half-priced taxi rides that are subsidized by VCs there is not a lot of competition. At real prices, there is nothing to stop the yellow cabs or somebody else in a town from making their own ride hailing app so you not only have competition from big players like Lyft but also many smaller players.
(E.g. I have no smartphone and no Uber app but when I have to leave my hotel/AirBNB at an ungodly hour to go to the airport I have no trouble reserving a ride from somebody the night before.)
It's not credible that Uber will be dominant in self-driving cars since everybody from Google to General Motors will get a piece of that. (e.g. nobody is going to have a complete set of patents, there will be cross licensing...)
This article on Bloomberg seriously misrepresents the situation with Uber:
https://www.bloomberg.com/news/features/2018-09-27/masayoshi...
That is, he's not competing with Sand Hill Road, he's buying what they sell and making it possible for them to look like they are successful at what they do. If he can find "greater fools" to buy into an Uber IPO he may do OK, but if he can't he might have to commit Seppuku.