It's fairly basic game theory and strategy. If it's not empirical enough for you then Economic theory in general might not make the cut either :)
Even in non-empirical economic theory, the idea doesn't sound particularly obvious or sound to me. Obviously predatory pricing by a large firm can drive small firms out of business, but the large firm doesn't actually make profit from that until they raise their prices again, which sends a signal to others to start competing. And yes, there are barriers to entry, but it doesn't seem like the resources a small firm spends to enter a market would be destroyed when that firm gets driven out of business by the large firm's predatory pricing. Assets will get liquidated, sold to someone else, and potentially used to start competing again when the large firm raises its prices.
Price wars can be horrible for consumers, that's why some forms of them are illegal[0]. If Lyft and Uber talk to each other about gutting prices to put cabs out of business it's illegal. If they read the same econ books and independently come to the conclusion that it's the best thing to do, it's legal.
We regulate the cab industry to insulate it from this type of thing, because once the high prices and bad service that come with market concentration happen it may be months or longer before better options become available.
[0] - http://en.wikipedia.org/wiki/Predatory_pricing