When I was younger, I heard an analogy about rowing teams. The strategy for winning races was to focus on your own behavior. The moment you started checking out the competition, you lost a bit of time and concentration.
I'd like to think that's how I approach work: success comes from focusing on my own work and providing value, surrounding myself with the best people and encouraging them to do their best. Not from actually fighting with the competition.
I'm with Random, that I'm not fond of the zero-sum game analogy. I think different people have different approaches to business and competition. For instance, at my husband's work they used a type of personality test that I'd never seen before - one of its components was judging how competitive/ruthless or caring/supportive a person was. The CEO of that company (one of Australia's largest banks) was a caring/supportive person - previously all CEO's had been the ruthless/competitive type. I know personality tests can be flawed but I think you can be successful in a business environment regardless of your appetite for conflict.