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Economics of love: Rejection worth chance at dream date

Anton Cheremukhin and Antonella Tutino

In a scene in the 2001 film A Beautiful Mind, the great mathematician John Nash discusses with friends the strategies of approaching women. If all the men approach the most-attractive woman in the bar, they will compete for her attention, get in each other’s way and lose the opportunity to meet other women, he opines. However, if the men coordinate their efforts and each approaches a different woman, they can increase the likelihood of all acquiring a date by the end of the night.

This logic was later formalized in economist Gary Becker's "A Theory of Marriage," becoming a hallmark of economic theory. Its main prediction holds that both men and women can be objectively ranked by some trait or index of attributes, which could include education, income and age—"attractiveness," for short.

The best social outcome is when they are matched assortatively; the most-attractive man matches with the most-attractive woman, the second most attractive with the second, and so on down the ranking (Chart 1).

Chart 1: Assortative Matching Provides Optimal Results

Matchmaking in a Nash equilibrium

In such a matching, no man or woman wants to deviate from his or her choice of mate because all the more-attractive potential partners are already taken, and the less-attractive ones are not in his or her interest. In other words, assortative matching is not only socially optimal, but is also what is called a "Nash equilibrium," a state in which each participant in a strategic interaction is acting optimally, given the choices of all the other participants.

With the advance of social networks and increasing prevalence of online dating, the question of how men and women match up has gained importance in economics and society. With unprecedented access to data collected through surveys and online dating platforms, it is possible to see whether Nash's intuition and its formalization through mainstream economic theory still hold up.

Aiming above your relative standing

Surprisingly, recent studies of data from online dating platforms document that men and women target partners that are ranked much higher than themselves in the desirability hierarchy. In other words, it seems as though everybody is seeking the most-attractive person in the bar. If the goal of dating is to match up, why is this happening? Is there a disconnect between mainstream economic theory and the practice of matching?

We argue (in a paper with Paulina Restrepo-Echavarria of the St. Louis Fed) that the seeming disconnect between data and theory disappears if we challenge the assumption from the classical theory that both men and women can perfectly distinguish each other when searching for a match. Our theory turns out to be relevant not only for dating behavior, but it also can be applied to census data to shed light on the determinants of marital sorting by factors that include income, education and age.

Making rational choices with limited information

We postulate an environment where all people in search of a mate have a limited attention span and lack time to vet in detail all the relevant characteristics of potential partners. For instance, if the desirability of a person is measured in terms of "attractiveness," as in the case of Nash's bar example generations ago, neither men nor women may be able to perfectly differentiate potential partners. They make mistakes in picking the most desirable among the group of potential matches.

The core of the argument rests on the fact that both men and women are aware that all potential partners are bound to make some mistakes in selecting a match if time, effort and attention prevent them from a thorough and exhaustive vetting process. Under these circumstances, a man who is not "attractive enough" may think he may have a chance to approach a more-attractive woman in the bar, counting on the fact that she may not be able to perfectly distinguish him from a more-desirable guy.

Generally, if the most-attractive woman will not be able to tell with certainty who is the most-attractive man, with some probability she will instead be attracted to the second-ranked man, with some probability to the third-ranked man, and so on. When men know that they have a chance with any woman, the potential benefit of being with the most-attractive woman will more than compensate for the admittedly lower probability that she will pick him rather than somebody else. Men find it optimal to target the most-attractive women in their search for a partner.

The exact same mechanism will work for women. The most-attractive man will not be able to perfectly distinguish among women, and with some probability pick the second-, third- or fourth-most-attractive woman. This implies that each woman has a chance with the most-attractive man. If the benefit outweighs the lower probability, in equilibrium, everybody is targeting the most-attractive partner.

This equilibrium-sorting pattern is illustrated in Chart 2: Both men and women target the most-attractive partner.

Chart 2: Targeting the Sub-optimal Partner in Equilibrium

Who matches with whom?

Our theory can rationalize several dimensions of the data. Whether everybody is going for the most-desirable candidate and to what extent depends on how differently or similarly people evaluate potential partners.

Men and women possess different characteristics—appearance, age, education, income and native language. Each person might be ranked high on some characteristics and low on others. Instead of having a universal attractiveness scale, each person might have different scales for different characteristics. For instance, people might value in others the characteristics they have themselves. If that is the case, they will match up by similarity instead of going for the most-popular partner, and matching may still be assortative as illustrated in Chart 1.

How people value each other by each characteristic and how this affects who matches with whom is an empirical question. Our theory of targeted search allows us to evaluate these patterns quantitatively by looking at the matching rates between populations of men and women broken down by combinations of demographic characteristics.

Looking at the resulting patterns through the lens of the model can help disentangle these motives for the U.S. population. We will discuss marital sorting by income and the effects this sorting has on household income inequality in a follow-up article.

About the Authors

Anton Cheremukhin

Cheremukhin is a senior research economist in the Research Department at the Federal Reserve Bank of Dallas.

Antonella Tutino

Tutino is a senior research economist in the Research Department at the Federal Reserve Bank of Dallas.

The views expressed are those of the authors and should not be attributed to the Federal Reserve Bank of Dallas or the Federal Reserve System.

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