I really...like really am not the person to speculate credibly in this area...but so long as people want to have a discussion I do enjoy hypothetical speculations :)

But...let's remember first that my intent is not to make claims...I am merely continuing a mental exercise in speculation/critical thinking.

Forgive me if I am over simplifying, but the example you forward is a traditional take on perfect competition.

But I don't think that we should discount the possibility of a lack of competition in this theoretical market. First, Price Discrimination itself requires that the firm doing the discriminating has some degree of monopolistic control/power in the market [1]. The existence of any price discrimination precludes the presence of effective competition in a market.

I think the Uber market is one that already exhibits signs of imperfect competition given the plethora of competitors that have struggled to find a footing:

* https://techcrunch.com/2016/11/08/uber-competitor-karhoo-shu...

* http://austininno.streetwise.co/2016/11/30/scoopme-an-uber-c...

* https://qz.com/583498/uber-competitor-sidecar-is-shutting-do...

Let's further suppose that Uber chooses not to pocket the revenue from this price discrimination immediately and instead re-invests it in the short term to establishing a Network Externality [2].

> Network effects become significant after a certain subscription percentage has been achieved, called critical mass. At the critical mass point, the value obtained from the good or service is greater than or equal to the price paid for the good or service.

If they keep it up long enough they should be able to slowly grind competitors out of the market. And while they might actually succeed in creating a monopoly, they don't have to in order to start rent-seeking [3]. Arguably, they already are doing so by increasing producer surplus with this price discrimination and widening the gap between rider cost and driver pay.

In this dystopian market state, Uber need not fear competitors because they could reduce their rent-seeking percentage to match or beat new entrants. They could also spread costs of undercutting local competitors to their entire user base (including raising prices on users it identifies using this price discrimination technique that would be willing to stomach the increase) which would allow them to potentially operate at margins unsustainable/unattainable for new competition. This would be a classic monopoly [4].

Now, there is nothing intrinsically bad about markets that have Monopolies...in fact there are some examples where it is more efficient to have a single supplier. But that is a different speculative discussion. I am just trying to explain why competition may not be an effective check to this practice.

TL;DR Uber's market likely already suffers from imperfect competition casting into doubt the effectiveness of competition to check this trend. Moreover, a firm might use price discrimination to carve out network externalities in amenable markets.

[1] http://www.economicsonline.co.uk/Business_economics/Price_di...

[2] https://en.wikipedia.org/wiki/Network_effect

[3] https://en.wikipedia.org/wiki/Rent-seeking

[4] https://en.wikipedia.org/wiki/Monopoly