Due to Uber's network effects you could say they'd have even greater power to change prices dramatically. Let's say Uber became the dominant transportation network in a particular geography and then trebled prices. Any new competitor has to both lure riders and drivers from Uber. Riders, sure they can be lured by cheaper travel but drivers want to earn the most money. Uber could simply double how much they paid drivers. All the existing drivers (and any new drivers) would rather work for Uber and get paid more. In fact they would have a vested interest in seeing the competitor fail.
1: https://en.wikipedia.org/wiki/Phoebus_cartel
2: https://en.wikipedia.org/wiki/Bell_System#Nationwide_monopol...
3: https://en.wikipedia.org/wiki/General_Motors_streetcar_consp...