There's evidence that all the big players have top talent, deep pockets, and are staying abreast of the research, which is humming along. Insomuch as they're committed, there's no good reason to believe any one of them is out of the running, or more than a couple years or so behind the peloton.
Because deploying Robotaxi fleets will be so capital intensive, no single company is likely to dominate the way Uber has in rideshare. There is enough demand spread out across enough different cities that they won't need to compete directly for a long time.
What Uber has, that all of the other players don't is a platform, data, and experience operating such a service. All they have to do is add in the self driving cars, whereas all (most) of the other players have to build the whole platform.
https://newsroom.uber.com/san-francisco-your-self-driving-ub...
https://www.theguardian.com/technology/2016/dec/16/uber-self...