This is a grossly over simplified assumption that does not stand on its own. The type of monopoly that Google has was not handed to it, but resulted from "nasty" competition. Google (currently) is literally too competent to beat in the search engine space. Perhaps Lyft will die off or by purchased by Uber, but it's not a given that it should, or even that it will.
More importantly, what happens when there is no competition between companies for drivers? Are we assuming that once (Uber|Lyft) has the market wrapped up they're going to benevolently maintain favorable driver pay rates? Are we really assuming that in the absence of incentives to do so that (Uber|Lyft) will favor drivers or riders instead of its own bottom line? Since this flies in the face of common sense and a mountain of empirical evidence to the contrary, why in this case is a monopoly preferred to competition?
So the answer isn't to prolong or encourage more competition, but to expedite the process going from competition to monopoly. There's no difference between a Lyft or Uber monopoly, but there's a huge difference between one of them winning, and both of them surviving.
No consumer wants to use two apps. No driver wants more pay cuts. Just like no advertiser wants to run campaign on two different search engines.
Hence why I said, one of them should win already.
Or you could let the free market allocate resources quasi-perfectly, let the prices fall and send the money you saved on that ride to an African kid who just lost his family to Ebola. I don't know how much an Uber driver should make, and neither do you, nor the government.
I think we should have a world in which all our cooperative efforts in markets and otherwise that lead to general wealth and resources, we then distribute them so that as many people as possible can live a healthy, secure, and dignified life.
This is why one of Lyft / Uber should die already and let the other take over the industry. Ride sharing is such an amazing idea, but the competition is nasty. This is a perfect example of why a monopoly is infinitely better than having competition: http://online.wsj.com/articles/peter-thiel-competition-is-fo...