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I would argue there isn't really a network effect for lyft or uber or any ride-sharing company for that matter. There might be brand and price effects for the companies to battle over amidst both riders and drivers.

I'd say there is a network effect for ride-sharing in aggregate, neither Lyft nor Ueber has been good at locking drivers and riders in with loyalty programs to try to keep people solely on their platform.

More drivers means faster pickups for riders, and more riders means less downtime for drivers. Drivers doing more rides per hour means they can be paid less per ride, lowering the price of a ride and further increasing demand. Sounds like a network effect to me. Offerings like Lyft Line and Uber Pool multiply both of these effects.

There is no cost for a driver to use multiple apps. There is no cost for a user to use multiple apps.

those reasons have largely boiled down to "lose money on each ride", that's not going to last.