Stable Relationships

TL;DR

This paper models the dynamics of relationships based on power balance, identifying conditions for stability that depend on dominance levels, with implications for social, professional, and diplomatic contexts.

Contribution

It introduces a dynamic model analyzing stability conditions of relationships based on power distribution, extending understanding of relationship dynamics across various contexts.

Findings

Stable relationships occur when both are dominant but below a certain power sum.

One dominant and one submissive can form stable relationships if dominance exceeds submissiveness within thresholds.

Stable relationships are impossible if both parties are submissive.

Abstract

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.