If someone is searching for you directly

I have a client who sells in a highly competitive product category and their product is a market leader. As a result their competitors target their own Google advertising at my client’s brand name to pick up people who are in market for the category. It gets really expensive to just advertise your own brand name, and its short-sighted compared to advertising to cold audiences. So what to do?
The trick here if you don’t want to spend ALL your budget just defending your turf, is to work out which types of people are most likely to buy and split your campaigns. If it is Women 35–44 in the top 50% income bracket, for example, then by all means seek to be #1 for this group. Let your competitors fight over the crumbs in other audiences.