  We study a dynamic model of the relationship between two people where the
states depend on the "power" in the relationship. We perform a comprehensive
analysis of stability of the system, and determine a set of conditions under
which stable relationships are possible. In particular, stable relationships
can occur if both people are dominant, but the sum of dominances is below a
bound determined by the model's parameters. Stable relationships can also occur
if one person is dominant and the other is submissive, provided the level of
dominance exceeds the level of submissiveness but not beyond a threshold. We
also conclude that a stable relationship is not possible if both people are
submissive. While our model is motivated by a social or romantic relationship,
it can also be applied to professional or business relationships as well as
diplomatic relationships between nations.
