To be blunt, yes, they can. Google doesn’t have any rules against bidding on branded keywords, regardless if it’s their brand or not. We understand how frustrating this can be when you are brand building. However, Google does restrict the use of trademarked names within their ad copy, though. When you work with Digital Logic, we will investigate and find ways to mitigate the effects of your competitors using your brand to promote themselves as best we can. Look at the bright side, they're helping you build your own brand awareness!