Successful love stories as differential games

Resumen

Understanding long-term romantic relationships poses a substantial problem in the social scienceswith enormous implications for the well-being of individuals in modern Western societies; see e.g.[2]. In particular, the keys to the proper functioning of stable and happy couples are not well known[1]. The difficulty of the problem depends in part on the fact that large longitudinal data sets ofmarital quality are scarce and noisy. In [3], a computational differential game model was introducedto synthesize long-term trajectories of stable and happy couples. How the long-term success of reallove stories depends on environmental or psychological factors remains essentially unexplained. Inthis paper, we analyze how successful trajectories depend on the cognitive processing of emotionalrewards and costs for both partners in the relationship. Our analysis draws on the differential lovegame modeling to carefully explore the sensitivity of successful outcomes (optimal control policies,feeling equilibria, and well-being) to the combinations of inputs that represent the cost and rewardsof partners. In particular, we show how the degree of heterogamy -i.e. the size of the gap betweenpartner contributions - affects the optimal solution to the problem of the couple.As a previous step, the statistical analysis allows us to determine a centralized reference trajectory of marital quality, using a longitudinal sample of more than 7000 subjects from 33 countriesobtained from survey data [4]. The data sample is used to determine a suitable parameter spaceso that the reference trajectory can be replicated by calibrating our model. This provides furtherevidence of the potential of the differential love game model to accurately describe real trajectories.Furthermore, we show how the feedback policies provided by the model allow us to estimaterealistic response times to recover a successful trajectory after external shocks of different sizes anddurations.