Alphabet and Uber view autonomous vehicles as using critical technology that may upend the automobile industry. Google started working on driverless cars around the time when Uber was formed, and Google is eager to prove that, despite its size and past successes, it can still innovate like a start-up. And replacing human drivers with self-driving cars would allow Uber to theoretically provide safer rides around the clock. Robot cars would also allow the ride-hailing service to avoid one of its biggest headaches — its drivers.

“There’s an urgency to our mission about being part of the future,” Travis Kalanick, Uber’s chief executive, said in an interview in August after announcing Otto’s acquisition. “This is not a side project. This is existential for us.”

Engineers like Mr. Levandowski are part of a limited pool of people with the experience and capability to lead efforts on self-driving cars. They are wooed by traditional automakers looking to acquire new technical talent and tech companies, both established firms and start-ups, who see the opportunity to use artificial intelligence and sensors to disrupt another industry.

“What’s in these people’s heads is hugely in demand,” because the talent pool “just doesn’t have enough miles under the wheels,” said Martha Josephson, a partner in the Palo Alto, Calif., office of Egon Zehnder, an executive recruiting firm.

In fact, Sebastian Thrun, who founded Google’s self-driving car project and is now the chief executive of the online teaching start-up Udacity, said last year that the going rate for driverless car engineering talent was about $10 million a person.