Some of this may come down to intrinsic vs. extrinsic motivation. A person who is driven internaly by the desire to win will be competative regardless of reward. For them, to win is the rewardand to lose or just place is fruitless. For someone who is extrinsicaly motivated to even compete, there must be some type of reward. Whether it is a bonus,promotion,recognition,etc.
So is the competition productive? If the goal is to sell more widgets, and more widgets are sold, and the profit is not lost on the bonus, then that is a productive competition.If it erodes workplace comeraderie, incites backstabbing and alienation, then it may not be productive.
If a win at all costs attitude takes hold and the cost is one of the companies better assets as an employee, then it can actualy be very counterproductive.
A book I read recently delves into this from a psychiactric perspective.It is called “Put Offs And Come-Ons” Psychological Maneuvers and Strategems by Arthur Harry Chapman.
Chapter 7- Business and Professional Maneuvers and Strategems, May the Best Man Win, pp143-148.