Isn't Uber's entire business model (and its ridiculous valuation) based on the idea that they were going to become a monopoly? (and thus recoup the huge investment costs by raising fares?)
I can't see them accepting a competitor in the long term. A competitor will keep margins slim and the VCs invested in Uber won't be very happy with that. I wouldn't be surprised if Uber ups the ante and cuts fares to absurd levels in order to try to drive Lyft into the ground.