So can Uber, that's just a race to the bottom.

Assuming that Uber has a competitive advantage because of their brand, and both Uber and Lyft are rational actors who want to maximize their profits, they will end up in a state where Uber has higher margins than Lyft.

> Assuming that Uber has a competitive advantage because of their brand

Woah - I see Lyft as the one with the competitive advantage due to Uber's brand. Uber is toxic while Lyft is seen as friendly.