Thats not competition! Thats just gonna make your work look better. Use it as a impetus to step up, improve and prove how much better you are.
Treat customers right, charge sensible prices, don't get drawn into a price war, do the best work you can, know your limits and be OPEN for business - put the hours in. Trust me - the work will come..... I should know, there were three tattoo studios in my town when I started, there are now seven studios and loads of scratchers. But we are still busy cos we make sure we are the best.
And remember, its easy to shine when you're surrounded by s&!t!!!