It won't work that way though. Cities have this thing called "rush hour" for a reason: a some specific times of the day far more people need to get around than others.
Worse, the people who use their car in the middle of the day are the least likely to use shared cars. They are the most likely to need a change of clothing, a stroller in their car just in case. They are also the most likely to run back and for from their car for each purchase at the mall.
What that leaves is people going to/from work, and their lunch breaks. At this point you may as well own your own car self driving car: at worst it is not much more expensive (shared might be 10% cheaper), and you get to leave your golf clubs in the car while at work. At best you can ignore a few tears and keep the car for longer making owning your own car cheaper than a shared car which needs to maintain appearance and cleanliness standards.
Shared cars work well for those people who rarely use a car. However those are the people who already are renting cars, using taxis and the like for the few times they need a car.