There is a similar effect with tollways. People often have a choice between using the tollway (and paying the toll) or taking the public roads and sitting in traffic.
I don’t have the figures for the USA, but here in Australia the rate people empirically use to avoid tolls is $12 per hour (i.e. they will sit in traffic for an hour extra to save $12 in tolls). Assuming people apply the same thinking to ride sharing, then a cheaper competitor with worse coverage should be able to capture a reasonable share of the market.
To poke a hole in my original comment, presuming that the vehicles are still being driven by humans, there should be a hard floor in how low the price can go. If Uber is already at the a point in some markets where the drivers earnings can't even make up for vehicle depreciation & gasoline, that floor may have already been reached. At that point competitors may have both the same or higher price point and be slower than Uber.
Once driverless vehicles are brought in to the market, presumably these dynamics change again.
A third variable is the device which retrieves a vehicle. Google & Apple, the platforms where presumably almost all Uber vehicles are called from (not sure how many people are using the SMS feature or if it is still functional), are both working on producing vehicles. The current assumption is at least Google's will be self driving from day 1 and both may operate in a manner more like Uber than a traditional automobile business model.
There is a lot more certainty around how transportation will look, in general terms, by 2025 than who will be collecting the profits from it.
Yes there is a hard floor with the price, but there are two ways it could go lower even without driverless cars. The first is Uber's indirect vehicle costs (borne by the driver, but ultimately affecting the price floor) are very high. The drivers don't have any economies of scale in running and servicing their vehicles. A competetor that is optimised for running costs could undercut Uber.
The second way a competetor could undercuts Uber is by accepting a lower return on capital. Uber's cost of capital is very high compared to the cost of capital in the utility industry. It will be very hard for Uber to compete long term against a rival with low cost capital.
My expectation is Uber will win the battle against its venture backed rivals and will lose to a new competetor optimised for running and capital costs.
I don’t have the figures for the USA, but here in Australia the rate people empirically use to avoid tolls is $12 per hour (i.e. they will sit in traffic for an hour extra to save $12 in tolls). Assuming people apply the same thinking to ride sharing, then a cheaper competitor with worse coverage should be able to capture a reasonable share of the market.