I have made my prediction that Uber will buy Lyft within three years. Someone did note also, on LinkedIn, that car companies can band together and take it off the public market. Largely, it will be hard for Lyft to thrive in a world of Uber. Alliance of car companies buying Lyft to deepen their ridesharing future is a better possibility since Uber buying can hit antitrust challenges.
On July 14 2017 (see video), I made a case that Uber will merge/acquire Lyft. As Lyft loses steam, post-IPO, and Uber coming to party, the pressure will heat up on Lyft. Then Lyft will surrender, and Uber will buy it within three years. Similar rivalries have ended together: Elance/Odesk (now UpWork), Groupon / LivingSocial, Sirius / XM and Rover / DogVacay.
These numbers below are from Uber and Lyft respective Securities and Exchange Commission Form S-1s.
Uber: $11.3 billion
Lyft: $2.2 billion
Uber: $1.85 billion (Adjusted EBITDA loss)
Lyft: $911 million
Uber: 700+ (globally)
Lyft: 300+ (across U.S. and Canada)
2018 Booking revenue from ride-hailing service
Uber: $41.5 billion
Lyft: $8.1 billion
Users in 2018
Uber: 91 million (including other services like Uber Eats)
Lyft: 30.7 million
Drivers in 2018
Uber: 3.9 million
Lyft: 1.9 million
Rides in 2018
Uber: 5.2 billion (includes scooter and bike rides, Uber Eats deliveries)
Lyft: 619 million