Generally, regulatory interactions between states are modeled as a coordination game of the battle of the sexes (BOS) type. BOS captures an important aspect of regulatory policy coordination. Its symmetrical nature is an expression of the assumption that both states care equally about a coordinated outcome but prefer a different outcome. However, this assumption leads us to ignore differences in the degree to which states prefer coordination. One state may have much stronger preferences for a coordinated outcome than another state. In this paper, I develop a model explaining how introducing variation in the degree of preference for coordinated outcomes, by influencing states preference rankings, may strongly change the strategic game that is being played at the international level. The weight states accord to coordinated outcomes will affect the power relationship between states and in this way will have an important effect on the selected coordinated outcome. Through a formal model, I show how the degree of preference for a coordinated outcome in both states determines whether the game is BOS, deadlock or an asymmetric game. In addition to this formal model, the paper discusses which elements in the domestic societal constellation might affect the preferences for a coordinated outcome.
