In this master’s thesis, we explore how mathematics can contribute to understanding the search for the right partner and the building of a happy and stable marriage. The key question is why, despite the desire and planning for a lasting relationship, such a large share of marriages ends in divorce. The thesis provides a review of mathematical literature that explains and models romantic relationships in various ways. To analyse the dynamics of relationships with respect to the partners’ personality traits, models of dynamical systems are used. We begin with a simple linear model and then gradually include psychological factors, environmental influences, and elements of modern society. This offers insight into whether a relationship is stable or unstable, as well as how it develops over time. A model based on the second law of thermodynamics and optimal control theory proves to be crucial for a long-term happy marriage, as it emphasises the need for continuous investment of just the right amount of effort in the relationship. Since our decisions are also influenced by those of the other partner, relationships can be convincingly explained through game theory. The optimal strategy for a long-term successful relationship is the tit-for-tat strategy, which clearly demonstrates how to respond to a partner’s actions in order to build a stable and fulfilling relationship. By applying the prisoner’s dilemma and the stag hunt, we show that trust and cooperation are essential for a lasting relationship.
|
