It can involve simulated cooperation, combined with actual opposition. Most relations involve partial cooperation and partial opposition. Similarly, position can also be defined this way. After all, it is people in positions of power, whatever that power may be, who have the ability to get things done. In society, this kind of power consists of the ability to move people toward certain ends, and command resources, to get things done.
Power is the power over other people.
In this sense, power, like image, is a position in a social network, so power and position bear a close relation. It is what can you do in relation to others and, when it is exercised, it is what you actually do. There are situations that resemble relations of inequality, in which the one in the dominant position doesn't have the power to control the other' s behaviors. I'm thinking of news interviews, in which journalists pummel public figures with embarrassing questions and the public figures are put on the defenses, in the losing position. And yet there isn't exactly an ability to coerce any kind of behavior.