Controlling forever love

  1. Herrera de la Cruz, Jorge
  2. Rey, José-Manuel
Revue:
PLOS ONE

ISSN: 1932-6203

Année de publication: 2021

Volumen: 16

Número: 12

Pages: 1-14

Type: Article

DOI: 10.1371/JOURNAL.PONE.0260529 GOOGLE SCHOLAR lock_openAccès ouvert editor

D'autres publications dans: PLOS ONE

Objectifs de Développement Durable

Résumé

A stable and rewarding love relationship is considered a key ingredient for happiness in Western culture. Building a successful long-term relationship can be viewed as a control engineering problem, where the control variable is the effort to be made to keep the relationship alive and well. We introduce a new mathematical model for the effort control problem of a couple in love who wants to stay together forever. The problem can be naturally formulated as a dynamic game in continuous time with nonlinearities. Adopting a dynamic programming approach, a tractable computational formulation of the problem is proposed together with an accompanying algorithm to find numerical solutions of the couple’s effort problem. The computational analysis of the model is used to explore feeling trajectories, effort control paths, happiness, and stabilization mechanisms for different types of successful couples. In particular, the simulation analysis provides insight into the pattern of change of both marital quality and effort making in intact marriages and how they are affected by certain level of heterogamy in the couple. © 2021 Herrera de la Cruz, Rey. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

€ Voir financement

Information sur le financement

Financeurs

  • UCM-Santander
    • PR108/20-14
  • RCC-Harvard
    • RCC_STF_2018_UCM_007

Références bibliographiques

  • Murdock GP. Social Structure. New York, NY: Free Press; 1949.
  • Coontz S. Marriage, a history. New York, Viking; 2005.
  • Dunbar R. The science of love and betrayal. Faber and Faber, London; 2012.
  • Carr D. The Linked Lives Principle in Life Course Studies: Classic Approaches and Contemporary Advances. In Alwin Duane F; Felmlee Diane H; and Kreager Derek A Editors (2018) Social Networks and the Life Course Integrating the Development of Human Lives and Social Relational Networks. 2018; p. 41–63.
  • Easterlin RA. Explaining happiness. Proceedings of the National Academy of Sciences. 2003;100(19):11176–11183. pmid:12958207 View ArticlePubMed/NCBIGoogle Scholar
  • Kahneman D, Diener E, Schwarz N. Well-being: Foundations of hedonic psychology. Russell Sage Foundation; 1999.
  • Proulx CM, Helms HM, Buehler C. Marital quality and personal well-being: A meta-analysis. Journal of Marriage and Family. 2007;69:576–593.
  • Kazdin AE. Encyclopedia of Psychology (Editor). American Psychological Association and Oxford University Press; 2000.
  • Bachand LB, Caron SL. Ties that bind: A qualitative study of happy long-term marriages. Contemporary Family Therapy. 2001;23(1):105–121.
  • Amato PR, James SL. Changes in Spousal Relationships over the Marital Life Course. Alwin Duane F; Felmlee Diane H; and Kreager Derek A Editors (2018) Social Networks and the Life Course Integrating the Development of Human Lives and Social Relational Networks. 2018; p. 139–158.
  • Sternberg RJ. A triangular theory of love. Psychological Review. 1986;93:119–135. View ArticleGoogle Scholar
  • Gottman JM, Murray JD, Swanson CC, Tyson R, Swanson KR. The mathematics of marriage: Dynamic nonlinear models. MIT Press; 2005.
  • Rinaldi S, Della Rossa F, Dercole F, Gragnani A, Landi P. Modeling love dynamics. vol. 89. World Scientific; 2015.
  • de Sousa R. Love. A very short introduction. Oxford University Press; 2015.
  • Dercole F, Rinaldi S. Love stories can be unpredictable: Jules et Jim in the vortex of life. Chaos. 2014;24(023134):1–6. pmid:24985448 View ArticlePubMed/NCBIGoogle Scholar
  • Rey JM. A mathematical model of sentimental dynamics accounting for marital dissolution. PloS one. 2010;5(3):e9881. pmid:20360987 View ArticlePubMed/NCBIGoogle Scholar
  • Pujo-Menjouet L. Le jeu de l’amour sans le hasard. Mathématiques du couple. Éditions des Équaters; 2019.
  • Finkel EJ. The All-or-Nothing Marriage. How the best marriages work. Penguin Random House; 2017.
  • Beck AT. Love is never enough. Harper and Row, New York; 1988.
  • Gottman JM, Silver N. What makes love last? Simon and Schuster; 2012.
  • Gottman JM, Silver N. The Seven Principles for Making Marriage Work. Harmony Books, NY; 2015.
  • Kippen R, Chapman B, Yu P, Lounkaew K. What’s love got to do with it? Homogamy and dyadic approaches to understanding marital instability. Journal of Population Research. 2013;30:213–247.
  • Byrne DE. The attraction paradigm. Academic Press; 1971.
  • Rosenfeld MJ. Who wants the Breakup? Gender and Breakup in Heterosexual Couples. Alwin Duane F; Felmlee Diane H; and Kreager Derek A Editors (2018) Social Networks and the Life Course Integrating the Development of Human Lives and Social Relational Networks. 2018;30:221–243.
  • Jacobson NS, Margolin G. Marital therapy. Mazel, New York; 1979.
  • Fisher H. Why we love. The nature and chemistry of romantic love. Henry Holt & Co., New York; 2004.
  • Van Laningham J, Johnson DR, Amato P. Marital Happiness, Marital Duration, and the U-Shaped Curve: Evidence from a Five Wave Panel Study. Social Forces. 2001;79(4):1313–1341.
  • Rey JM. Sentimental equilibria with optimal control. Mathematical and Computer Modelling. 2013;57(7-8):1965–1969.
  • Bauso D, Mansour DB, Djehiche B, Tembine H, Tempone R. Mean-field games for marriage. PloS one. 2014;9(5):e94933. pmid:24804835 View ArticlePubMed/NCBIGoogle Scholar
  • Dockner EJ, Jorgensen S, Van Long N, Sorger G. Differential games in economics and management science. Cambridge University Press; 2000.
  • Goudon T, Lafitte P. The lovebirds problem: why solve Hamilton-Jacobi-Bellman equations matters in love affairs. Acta Applicandae Mathematicae. 2015;136(1):147–165.
  • Herrera de la Cruz J. Numerical resolution of deterministic and stochastic differential games in feedback Nash equilibria. Complutense University of Madrid, Spain; 2020.
  • Herrera de la Cruz J, Ivorra B, Ramos ÁM. An Algorithm for Solving a Class of Multiplayer Feedback-Nash Differential Games. Mathematical Problems in Engineering. 2019;2019.
  • Holt CA, Roth AE. The Nash equilibrium: a perspective. Proceedings of the National Academy of Sciences USA. 2004;101(12):3999–4002. pmid:15024100
  • Gottman JM. The science of trust: Emotional attunement for couples. WW Norton & Company; 2011.
  • Whyte MK. Dating, mating, and marriage. Routledge; 2018.
  • Basar T, Olsder GJ. Dynamic noncooperative game theory. vol. 23. Siam; 1999.
  • Bressan A. Noncooperative differential games. Milan Journal of Mathematics. 2011;79(2):357–427.
  • Jørgensen S, Zaccour G. Developments in differential game theory and numerical methods: economic and management applications. Computational Management Science. 2007;4(2):159–181.
  • Bardi M, Capuzzo-Dolcetta I. Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Springer Science & Business Media; 2008.
  • Falcone M, Ferretti R. Semi-Lagrangian approximation schemes for linear and Hamilton-Jacobi equations. vol. 133. SIAM; 2013.
  • Mai-Duy N, Tran-Cong T. Approximation of function and its derivatives using radial basis function networks. Applied Mathematical Modelling. 2003;27(3):197–220.
  • Fasshauer GE. Meshfree approximation methods with MATLAB. vol. 6. World Scientific; 2007.
  • Kulu H. Marriage Duration and Divorce: The Seven-Year Itch or a Lifelong Itch? Demography. 2014;51(3):881–893. pmid:24493065 View ArticlePubMed/NCBIGoogle Scholar
  • .Xu Q, Qiu Z, Li J. Is the “seven-year itch” real?—a study on the changing divorce pattern in Chinese marriages. The Journal of Chinese Sociology. 2016;3(17):1–23.
  • Frisco ML, Williams K. Perceived housework equity, marital happiness, and divorce in dual-earner households. Journal of Family Issues. 2003;24(1):51–73.
  • Birditt KS, Hope S, Brown E, Orbuch TL. Developmental trajectories of marital happiness over 16 years. Research in Human Development. 2012;9(2):126–144.