If you live in a city, chances are you’ve got a taxi app on your phone. Right now, there are a number of choices: Lyft, Sidecar, Uber, and a few others. But imagine a future where there is only one option — and all the traditional taxis have been driven out of business. A time when if you need a cab somewhere, it’s Uber or bust. Imagine further that sophisticated pricing algorithms have enabled the company to determine exactly how much you’d be able to pay for a ride.

This might all sound implausible, when Uber and Lyft are locked in ferocious rate-cutting wars and trying to poach each other’s drivers. But there could easily come a time when one finally defeats all its competitors. It could be any of them, but the smart money would be on Uber, a notoriously aggressive company, scornful of existing legal regimes or industry norms that has already captured much of the taxi business.

With traditional cab companies collapsing and most cities reticent to tackle ride-sharing apps head on, Uber would have a chance to dominate the American taxi market to an unprecedented degree. And because any such nationwide taxi monopoly would also have powerful high-tech tools at its disposal, it could be the first company in history to be able to attempt perfect price discrimination — adjusting individual prices so that every taxi customer pays as much as she can afford.