Daniel Gross has published an interesting NBER working paper titled, "Creativity under fire: The effects of competition on creative production." Gross writes the following in describing his key findings:
This paper studies the incentive effects of competition on individuals’ creative output, exploiting a unique field setting where creative activity and competition can be precisely measured and related: tournaments for the design of commercial logos and branding. Using image comparison tools to measure originality, I show that intensifying competition both creates and destroys incentives for creativity. While some competition is necessary to induce high-performing agents to develop original, untested designs over tweaking their existing work, heavy competition discourages effort of either kind.
The key idea here is that a certain amount of competition can encourage people to continue exploring original ideas, rather than simply becoming conservative and making only incremental changes to previous work because of positive initial feedback. Of course, as Gross notes, the ability to find just the right level of competition to properly motivate creative work is very tricky. He describes the challenge of achieving the "Goldilocks" level of competition - just balanced in the optimal way. It's hard to do. The paper is interesting, nonetheless, because it seems to counter some arguments that have been made in the past suggesting a simple negative relationship between competition and creativity. In short, those past arguments tend to be very negative toward extrinsic rewards and favor methods for fostering intrinsic motivation as a means of encouraging creative work. They favor collaboration over competition. Gross' work suggests that competition can play a favorable role, but only if managed carefully.