This. You get what you incent. If people are rewarded for working together, they will work together. If they are rewarded for individual contributions, they will optimize for that.
Now, it can be tough to measure and reward team effort, bit if that is what is important, figure it out!
Anecdote time! When I was a student, performance scolarships at my faculty were distributed this way. There were set thresholds, and if your grade average from the previous year was above a given threshold, you got +X money in scolarship. We were all extremely cooperative. People helped each other all the time, we pooled notes, scans, bootleg textbook pdfs, previous year's exam questions, we passed this knowledge down to younger students, who in turn passed them further after adding more materials of their own. We'd happily help each other get better grades.
You bet there was a lot of us on those scolarships. And people who came from the outside were extremely surprised about how friendly and helpful everyone is.
After I left, my faculty was forced to make scolarships work the way they work at every other faculty/university - i.e. make only top X% of students eglible for rewards. This instantly killed teamwork dead. I know few people who are still studying and they say there's a clear and visible difference now. People no longer share things. They don't care about recording exam questions for others, they don't coordinate the whole year to win something. Students stick to small groups and are antagonistic to others. If they help at all, they do it to the degree it doesn't endanger their own chance for scolarships.
Incentives matter. Also greed/stupid costs savings on the part of people setting up incentive structures matter too.
That is an interesting idea and it probably works in some rare situations. But unfortunately, most of the time, we only have limited resources and so a limited prize pool. The question, for managers/politicians/capitalists, usually is how do we get maximum motivation out of a limited rewards budget.
In the general case, the goals of the company and the employee are not always aligned so I don't think this is an easy problem to solve.
More specifically, the goals of each team member are not always aligned either, so trying to incent an entire team of people who don't have the same goals doesn't always work.
It's more likely to do so the bigger the team. In a team of 500, someone might think "my personal contribution doesn't matter much", but they are less likely to think so in a team of 5. Furthermore, in small teams social pressures are likely to deter free riding.
> In the general case, the goals of the company and the employee are not always aligned so I don't think this is an easy problem to solve.
Yes. It's the principal-agent problem -- http://en.wikipedia.org/wiki/Principal%E2%80%93agent_problem