We need robots than.
Although it would be interesting to go "you must have a space where a person can fit, and if you ever kill the dummy inside you lose the race" (defined a little more precisely, of course).
Remember: you probably want to keep the scale vaguely car-size. That way you'll get the most applicable innovation coming out of it. And also that way it'll tend to be the most interesting to spectators.
Instead of the company with the most money, the driver skill is more important this round.
http://www.fiaformulae.com/en/news/2015/february/eight-manuf...
They look the same in the way a Lenovo and an Apple look the same.
There are rules on track and wheelbase, crash structure and aero wing size that tend to dictate the overall silhouette, but from there, everything else is very different.