Each new car in your fleet has diminishing marginal effect to a passenger, and has negative effect for the other drivers. And you need to compete for both drivers and passengers.

This is why Uber and Lyft end up in driver subsidy cost wars.

Interestingly, the negative effect part is wrong for carpools, but that is not Uber's primary business (I'm assuming carpool drivers would rather be passengers)

That inflection point happens after you have a _lot_ of cars on the road, much more any new entrant will commit. It's equivalent to saying the power company gets diminishing returns from additional supply after they've built enough capacity to meet current demand. No one but the natural monopoly actually gets to that point.

That's a possibility. I'm not sure it's true. Both Uber and Lyft have good waiting times right now. The hypothesis that they will replace privately owned cars supposes that the market will grow immensely.

Waiting time is a function of: number of cars, size of the city, number of customers (to ignore congestion for now...) To have a good start as a new entrant, it's just a property of the size of the city. Then, you need to grow your fleet with your number of customers to keep waiting time constant. That number of cars to start with, the barrier to entry, is a tiny portion of what you need to add to keep up with demand.

If you don't have to compete with drivers, with autonomous cars, it's not that hard to meet and start a price war.

Again, I don't see how Uber will avoid being squeezed out of their margins the way airlines are. It's not cheap to start an airline, yet many people have done it. And all you need is 3 competitors to drive prices, and margins, down.