The main issue, as others have pointed out, is that the network effects and barriers to entry with Uber are quite low, so even if they beat Lyft they won't be able to jack up prices well above cost. In Austin, Uber and Lyft left after city voters passed driver fingerprinting requirements, and a flood of new companies entered the market. These new apps and companies had problems at first, but I currently use RideAustin (a non-profit, mind you) frequently, and despite being slightly more expensive than Uber is currently, the experience is pretty much indistinguishable.
The main issue, as others have pointed out, is that the network effects and barriers to entry with Uber are quite low, so even if they beat Lyft they won't be able to jack up prices well above cost. In Austin, Uber and Lyft left after city voters passed driver fingerprinting requirements, and a flood of new companies entered the market. These new apps and companies had problems at first, but I currently use RideAustin (a non-profit, mind you) frequently, and despite being slightly more expensive than Uber is currently, the experience is pretty much indistinguishable.