Over the long run, at least in the U.S. it seems like Uber/Lyft are edging towards a comfortable duopoly. Usually their prices move in lockstep (each has insights into the other company's prices through email receipt intelligence, credit card intelligence, webscraping, etc.). And their services are fairly exchangeable. For either one to win there needs to be either a massive cost advantage or some sort of stickiness…
don't discount the ability for either company to build that stickiness. They know this is important. Think credit cards, collaboration with last-mile transportation (Uber + Bird), discounts on restaurants, things of that nature. They can and are working towards building more of a brand ecosystem.
Who is going to pay for these discounts? Uber's investors?