Right now I get very low CPC on our trademark and very good conversion. I could triple my bids and still make a good return. I noticed that competitors are bidding on our trademarks and I understand Google's position on this. Should I try increasing my bid just enough to beat him or should I bid really high and force his cost up due to my higher quality score? My first goal is to be in the first ad position but I wouldn't mind driving his costs up.
I thought G did not allow trademark bidding in the US. So, can you not get your competitor blocked? Theoretically, you can bid as high as you like and you will only be charged 1c more than your competitor's max. CPC to appear above him. So, you could "max out" him/her on their current bid. If you are then appearing 1st and your max CPC is still within your bid limit you can leave it there and see what happens, i.e. whether he wishes to chase you or not and push up the costs. The other thing to remember is that with the new, coming, ranking system for placement above the natural results you should get placed there ahead of your competitor even if bidding less than him, assuming that since it is your trademark you should have much better QS and relevance. So, it might be worth hanging on until that kicks in.
Source (and more info): http://blog.brandverity.com/52/the-nuances-of-search-engine-ppc-trademark-policies/
This is what I was referring to although, as far as I am aware, it is not universal, e.g. it applies in the USA but not UK. I am not sure about other countries.