Benefits of marriage as a search strategy

Résumé : We propose and investigate a model for mate searching and marriage in large societies based on a stochastic matching process and simple decision rules. Agents have preferences among themselves given by some probability distribution. They randomly search for better mates, forming new couples and breaking apart in the process. Marriage is implemented in the model by adding the decision of stopping searching for a better mate when the affinity between a couple is higher than a certain fixed amount. We show that the average utility in the system with marriage can be higher than in the system without it. Part of our results can be summarized in what sounds like a piece of advice: don't marry the first person you like and don't search for the love of your life, but get married if you like your partner more than a sigma above average. We also find that the average utility attained in our stochastic model is smaller than the one associated with a stable matching achieved using the Gale-Shapley algorithm. This can be taken as a formal argument in favor of a central planner (perhaps an app) with the information to coordinate the marriage market in order to set a stable matching. To roughly test the adequacy of our model to describe existent societies, we compare the evolution of the fraction of married couples in our model with real-world data and obtain good agreement. In the last section, we formulate the model in the limit of an infinite number of agents and find an analytical expression for the evolution of the system.