What will happen is:
Companies will buy fleets of self driving cars.
The best self driving cars will be too expensive for most people to buy.
People will just pay one of those companies for transportation services.
The transportation - serving companies who will use the cars in the most efficient way will survive. They will use AI to optimize the usage of the fleets.
Regulators (governments) will tax the companies per km / time interval / peak hours.
People will pay more if they want to travel alone or want to travel in a straight line. They will pay more if they want more exact timing.
Roads will be safer because they will communicate with the cars and the cars will communicate with other cars.
There will be manned vehicles that will help relieve any obstructions.
In other words, given proper tax rules, transportation will regulate itself in effective and efficient ways.