Have you tried contacting the competitor and asking them nicely to stop? In my experience with this sort of thing, a polite call or email is most effective. If you email, make sure that what you wrote won't be embarrassing if they publish your email.
If they are intransigent, explain that you understand but, just so they know, you will be pursuing a Tit for Tat strategy: http://en.wikipedia.org/wiki/Tit_for_tat Communication really helps when you're tit-for-tatting, so contacting them will help on that front. If you are all relatively small, there are no antitrust issues at all.
If you are nervous about contacting them, you can pursue a tit for tat strategy anyway. To make it clear what you're doing, use the exact same copy that they do. If you want to be really direct, write a message to them in the ad copy.
In any case, you said they're bigger than you, so you'll actually get more leads from doing this than they get from keywords on your brand.
