"It was a video game? At the time I was so hung up on “Space Invaders” I was blind to all the other ones."
It was a table-top game. Steve Jackson games is still in business and they still sell it. Here is the web site, with a link to the Car Wars page.
http://www.sjgames.com/car-wars/
It was released in 1980, which fits with my memories of playing it with buddies from work in the mid-80s.
WOW! This is the first I have heard of it. It must be where the current crop of video game designers spent their time.