A Mathematical Theory for Optimal Marital Interactions

Abstract

The study of marriage dynamics and of strategies to reduce the likelihood of divorce has beenan important research area for decades. Gottman’s [15] research on successful marriages revealed three interaction styles: conflict-avoiding, validating, and volatile. There has not been progress in explaining how couples evolve into these styles of interactions and why failure to do so leads to failed marriages. The first chapter shows that the ubiquitous conflict-avoider style naturally arises through a couple maximizing a goal in their marriage when they do not consider an emotional cost. This leads to a mathematical optimal-control problem. In the second chapter, we present a differential-game-theory model where we explore what happens when spouses have different marriage goals. We also show that validating interaction-styles arise from the psychological cost of interacting with and/or ignoring one’s spouse. In the final chapter, we present strategies for marriage repair.