It is hard to step away from your conditioning. But when you are conscious of your actions and your ability to choose your response then you have a far better chance of subverting your competitive nature. It takes will power and hard work but it is possible.

There is also a very good talk on TED.com that uses the terms zero-sum game and non-zero sum game. It’s by Robert Wright, check it out here

I personally find it basically impossible not to ‘play’ it, without actually being aware of avoiding it. It seems very ingrained in nature, although nobody really benefits.
Aikido (a non-aggressive martial art), helped I believe, but as soon as I find myself being threatened, it will nethertheless turn back into a nullsummen spiel for me, especially if someone else is very focused on it.

Little steps I suppose. Anyway, I highly recommend Paul Watzlawick’s ‘self-help’ books, which are apparently considered radical counterparts to American self help books. I can’t say that for sure, but they’re at least very well-written and extremely helpful (eg doesn’t make you unhappy…)