Emotional Trade-Offs in Successful Romantic Relationships: A Differential Game Approach

Jorge Herrera de la Cruz and José-Manuel Rey ()
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Jorge Herrera de la Cruz: Department of Mathematics and Data Science, Universidad San Pablo—CEU, 28003 Madrid, Spain
José-Manuel Rey: Department of Economic Analysis, Complutense University of Madrid, 28223 Madrid, Spain

Mathematics, 2025, vol. 13, issue 23, 1-19

Abstract: Understanding the success of romantic relationships remains a complex scientific challenge with significant implications for modern Western societies. In particular, the mechanisms underlying successful relationships—those that are both long-term and emotionally fulfilling—are still not fully understood, especially regarding the role of psychological and environmental factors in shaping their evolution. This gap is partly due to the limited availability of long-term data on marital quality. In this paper, we use a differential game model to replicate the long-term dynamics of successful relationships. We analytically characterize how variations in each partner’s subjective evaluation of emotional rewards and costs influence key relational outcomes, such as equilibrium effort levels, overall happiness, and relationship quality. Through numerical simulations, we further explore how asymmetries in emotional processing between partners affect optimal effort policies and individual happiness. Notably, our results suggest that one’s own emotional traits exert a stronger influence on relationship satisfaction than those of one’s partner, aligning with findings from relationship science.

Keywords: romantic relationship; differential games; Nash equilibrium; differential equations; emotions; happiness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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