It is a great strategy for your competitors to buy your brand name on Google Adwords. You invested time and money into your brand name and they reap the benefits by showing their ad every time someone searches on your brand name.
Should you stop them? Not necessarily:
- If they are the bigger brand it may be smarter to advertise on their name and let them to continue to advertise on your name.
- Since they are better known you will get more exposure than they will.
If they are not advertising on your name should you advertise on their brand names?
You have to consider the legal issues. Consider this recent case from Israel, where Dr. Dov Klein won a court case against Google because his competitors in the plastic surgery field had bought Google Adwords using his name.
The case was interesting because the case was outside of the USA. This means that you may be exposed under different laws which apply in different countries. In the USA the courts take a different view. Read this long article to see how a USA court views this issue.
And the opposite is true. If you want to stop your competitor from using your brand name it may be worthwhile to start legal proceedings in a different country