What is your incentive to do that? I see that as the key. In a company, employees needs an incentive to work together and be constructive. They are not friends.
If you do not get that incentives, if your department success means less budged for mine, if my colleague success puts my job at risk, if your project success creates a problem for mine, I will not be motivated to collaborate.
If you create that incentive of collaboration then the "challenge" factor will be there. I have worked in great teams where we were evaluated as a company, where bonuses were for everybody or no-one. And it was a very competitive environment, I wanted to be as good as any colleague, know as much as they did. And, I wanted them to succeed because it was awesome to see such great projects but also because it was good for myself.
I have not found any healthy company were competition was enforced top-down. Only when collaboration is designed and encouraged top-down then healthy sportsmanship arise from great engineers and teams.