Here's a straightforward ideal-typical mathematical metaphor with a game-theoretic flavour. I simplify a bit, to make it easier to get into the spirit.
Assume two actors AA and BB and 4 future events w, x, y, z (which may be, among others, doing nothing). A has the following assumptions/preferences.
- AA thinks of him/herself as being able causally to bring about w or x
- AA prefers w over x.
- AA also prefers xy (standing for x and y) over wz.
- AA assumes that BB has y and z as behavioural options.
- AA expects that BB would react with y if AA does x, and BB would react with z if AA does w.
AA thus chooses action x rather then w, and attributes this choice to B's influence.
This structure of behavioural options, preference orderings and causal expectations is tersely referred to as "BB has power over AA". It's easy to generalise this definition to an arbitrary number of actors and actions.