Despite recent advances, no general methods for computing bargaining power in non-cooperative games exist. We propose a number of axioms such a measure should satisfy and show that they characterise a unique function. The principle underlying this measure is that the influence of a player can be assessed according to how much changes in this player's preferences affect outcomes. Considering specific classes of games, our approach nests existing measures of power. We present applications to cartel formation, the non- cooperative model of the household, and legislative bargaining.