I think there will be a mix of self-driving car producers and third party app developers trying to access this market opportunity. Whichever companies have the best mobile apps will dominate the market. Car manufacturers will make money either way and would likely end up with a competitive advantage.

Maintenance and storage depots are fairly likely to be outsourced or franchised, so those business models would be more accessible. The companies with the leading robotaxi apps might share ownership of the cars with the maintenance and storage depot business owners, but I feel it's less likely that individual people would be contributing their personal robo taxis the way Uber works. I think it would start with a company like Uber testing out purpose-made experimental robotaxis that Uber owns, and then they'd just keep buying more of their own purpose-built robotaxis. GM, or Tesla, or whoever starts making robotaxis specifically for this service might just make their own app and push out companies like Uber because the car manufacturers control access to the car's computer systems.

You could always buy stocks in companies that seem like they could dominate the future of the market, but I understand the preference for ownership of tangible capital, like your own fleet of cars to provide this service. Maybe think of some way to make a business out of the local services needed to support a national fleet, because that's the part that would be harder for GM, Tesla, or Uber to manage themselves.