Abstract
This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple’s network on their feeling states and their well-being.
Highlights
We look at marital interactions and relationships
We focus on a very ephemeral thing: what happens to the couple as they interact over time
We model the feeling state of a couple as a noisy differential equation influenced by random events, parents, children, friends and the social distribution of marital status, where the term ‘‘mean-field’’ refers to the distribution of couple feeling states in the society
Summary
We look at marital interactions and relationships. Here relationship refers to the unit (couple), rather than to the two persons. Our idea is to use mean-field games to capture the influence of society distribution of states on a generic couple. In their pioneering work in [3], Gottman et al have widely illustrated the importance of mathematical theory in the field of marital research. Stationary sentimental steady states are examined in [4,5] the context of infinite horizon discounted optimal control problems None of these previous works considered the influence of model uncertainty, noise, random events, and the social distribution of states (mean field). We describe the sentimental dynamics, define the payoff functional for the marital interaction and state the optimal control problem. We consider respectively an open-loop control problem, an optimal feedback strategy for the couple and a mean-field sentimental strategy
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