Probably none. By having an open system, prices will invariably get pushed down (better for end users) which will deincentivize drivers (worse for end users)

There may be some equilibrium somewhere, but I don't believe it will be in the users best interest having to wait for cars.

Just my thoughts. I'm probably wrong.

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.

In an open system, how do you ensure basic safety needs are met - eg, do drivers have licenses?

I sure as hell am not getting into a car with an unlicensed driver

a reputation system.

Once robo cars are here, it'll be game over. Google wins.