I think we'll see at least two main car providers in major cities plus some niche operators, then one major network that allows you to buy your own car to be committed to a pool as an investment.
Do you think we'll see public transit orgs (for example, PACE/CTA in Chicago and its suburbs) purchase their own self-driving vehicles to provide transit services?
This isn't just a city issue, but a country issue too. Vulnerability to both economic sanctions and espionage should be real concerns. You can take a look at the companies operating in Israel for an example of a market this would be an immediate concern. Likewise for companies operating in Washington DC. There are politicians and lobbyists regularly using Uber. Would this DC audience want to use Yongche, Kuaidi, or another Chinese service?
Another interesting consideration is who is building and selling these automated vehicles. Hypothetically a future Google building vehicles could acquire Uber and now they own the entire value chain.
A company such as Google could earn a substantial piece of the rider's revenue from advertising which would make it hard for competitors much like Yahoo & Bing under earned Google on search inventory. At that point it becomes very hard for competitors. Does ad based earnings sound unreasonable? Consider that companies, such as Delta, already are bidding their organic listings down on Google. They rank #1 for their name yet still buy the inventory. You could jump in the car and say KFC -- and KFC pays Google for the ride. Or you say "fried chicken" and Google gets even more money to take you to the nearest KFC (or may be Popeyes in that case.)
Secondly, consider additional activities in the vehicle. A car build to drive itself is going to be configured differently than a manned vehicle. May be a Facebook car arrives and you strap on the complimentary Oculus headset.
I don't know what it is, but don't discount the ability of a self driving car service to substantially differentiate itself beyond competitors in the future.
Any of these options will make it extremely difficult for public transit to compete. Certainly cabs are done without gifted monopolies. (Also worth considering if a self-driving cab company can retain any political power without having a fleet of human drivers)
Whether or not Uber is overvalued, they are taking the money. Probably the better choice. The US stock market keeps hitting highs, at some point there will be a drop, or may be a crises with junk debt (very low yields just like 07) and it is going to be a lot more difficult to raise money over night.
