By having an open system, since there is no longer a corporate middleman entity which takes a cut off a profit, and since anyone can compete, therefore prices will get pushed down. But just like any other perfectly-competitive system (https://en.wikipedia.org/wiki/Perfect_competition), the price in equilibrium will approach the marginal cost when marginal cost equals marginal revenue, not get pushed down indefinitely. I guess that would approximately equal to the market price of uneducated labor willing to drive plus the cost of the car+gas usage, insurance, etc. So price won't drop lower than what is needed to get people to actually drive the cars.

Now of course, maybe also need to be concerned about autonomous cars using this p2p app, in which case just need to pay a slave robot with the minimal energy it requires to drive.