And if Uber perfects self-driving cars if they are deluded enough to think they can replace their human drivers with a roving fleet of such... oh how childish and stupid that would be. I would give it 10 days before someone would introduce GUber which lets individuals with self-driving cars to time share them out when not in use via an app, destroying Uber swiftly and making every self-driving car they own (and maintain) a liability.
The only way I could see them remaining interesting for more than a couple more years would be if they developed an awesome self-driving car - and gave it away for free. With anyone who accepted one obligated to permit the thing to be time-shared out by Uber to provide rides when its not being used with X number of hours of availability given per month. That would be hard to compete with, whether through peer to peer or individuals renting their self-driving cars...