There is actually a reasonable amount of competition within the autonomous car space. A lot of people online only ever hear about Google's initiatives, but Audi, BMW et al. are building driving systems, some of which approach 100+ km/h.[1]
I definitely agree that more competition in the area is good. Hopefully as more players build these systems, they'll continue to improve and be commercialized quicker.
That's why I added "obvious", because even though there are a lot of autonomous efforts (large and small) from other companies, Google seems to be getting all of the attention.
Actually, several manufacturers have self-driving car projects[1]. some of them are even field-testing them in real-life situations, such as a driven leader truck being followed by other trucks[2].
So, I don't think it lacks competition for Google, who doesn't even build their cars - most probably they'll license the technology for other companies, and Tesla may well be one of them.
