Late marriage and transition from arranged marriages to love matches: A search-theoretic approach

ABSTRACT

The aim of this study is to explore the mechanism behind how the spread of individualism, the prevalence of love matches, and the increase in search costs affect late marriages in Japan. To this end, I construct a search-theoretic model, which is a combination of the Markov decision process and the evolution of preferences. I present three results. 1) The spread of individualism is driven by those who moderately consider the social status of their family. 2) The spread of individualism and the prevalence of love matches delay the average marriage timing, but its effect is limited. 3) The diversity of individualism prevents people from switching from love matches to arranged marriages, while the search costs are rising.

KEYWORDS:

• Mate selection
• arranged marriage
• individualism
• late marriage
• evolution of preferences
• markov decision process

Notes

¹ For instance, using the notation of assumption 6, the state reflects that the class of the candidate the player faces is the same as that of the player, and the candidate’s degree of individualism satisfies .

² In equation (1), holds when . Thus, when , means , and this holds when . Therefore, traditionalists () prefer arranged marriages to being single, and prefer being single to love matches. On the other hand, individualists (except ) tend to prefer being married to being single, regardless of the way of marriage.

³ When a player proposes to candidates, candidates always accept if they belong to the same class. This is because the utility of an arranged marriage is always greater than that of being single ( ).

⁴ In this model, the optimal strategy is obtained as below. In general, the long-term discounted utility satisfies the following formula (Stokey and Lucas 1989):

where is a set of states a player can reach in one step from state , and is the same as in assumption 9. Strategies and states are discrete, so this formula produces simultaneous equations consisting of seven equations. The solution to these simultaneous equations is the long-term discounted utilities . Blackwell (1962) shows that there exists an optimal strategy satisfying for all strategies . I compare between eight strategies and obtain an optimal strategy.

⁵ There may be several optimal strategies, but I did not observe such a situation.

⁶ This assumption is to ensure the simplicity of the model. Other parameter sets of fitnesses are shown in the appendix.

⁷ The long-term discounted fitness is also calculated as that of utility.

⁸ The results of analyses 2 () and 3 with other parameter settings are not shown because they indicate the same tendencies as those in the results in section 5.2.

⁹ I conduct the analyses for 3000 to 5000 periods. I vary the periods with the value of the basic probability to marry through love matches . If the shares of individualism and satisfy one of the following convergence conditions, the calculation stops; (1) and ; (2) or ; (3) , where . These conditions express that the dynamics have converged.

¹⁰ Related to the spread of individualism and the increase of the search costs, another analysis shows that individualism spreads till when the invading individualisms are and (, not shown).

¹¹ Strictly speaking, the share of individualism, which includes that of moderate individualism, affects the fitness. Thus, this discussion and Figure 12 do not change, even if we consider the share of all individualism ().

Additional information

Funding

This work was supported by the JSPS KAKENHI [Grant Number JP 16J00977,Grant Number JP 17H06594].