You just got to get over the fear of losing work, obviously your competition hasn't got over this fear yet.
I live in a smallish village, 810 houses, Ideally I would like a full time round here, it won't happen as I would need 500 out of those 810 houses unless I buy out the competition. I currently have 1 weeks work and working on building my 2nd week, if I get to this point I will be happy.
The village is already covered by half a dozen window cleaners, myself included, the chap with the biggest round only bought it before Xmas and is quite threatening to the other window cleaners when he loses jobs to them, he is currently one of 4 window cleaners touting for new business here mainly by under cutting, however none of them seem to be having much luck taking any of my customers of me, I have only lost 1, but have somehow managed to pick up 18 that they have failed to get since the start of the new tax year.
I don't doubt that they will pick up some customers but they won't get many, after a while they will fall by the wayside and the customers will become available again to whomever gets them first.