I’ve been thinking about another interpretation of the beauty vs message graph for men messaging women that I posted last week:

I was quite surprised that the men’s graph didn’t follow a Pareto distribution: the 20% most attractive women should have received 80% of the messages. I had to refresh my economics to understand why.

Consider the (unembeddable) bar scene from A Beautiful Mind. This excellent article explains the economics behind the scene. The scene is not an example of a Nash equilibrium, it’s an example of a coordination game.

A Nash equilibrium is when no one can improve their lot by a selfish action. A Pareto optimal outcome is where the total happiness of the group cannot be improved. In this case, the Pareto optimal Nash equilibrium is for one of the men to get the blonde and the other three to get brunettes.

The question is how to determine which of the men should go for her. Women set prices for themselves. Men, based on their attractiveness and other qualities, have “money” to spend on them. Think of the women as having probabilistic prices: a brunette is more likely to go home with an average man than the blonde; the blonde is more likely to go home with an above-average man than an average man.

The payout for every individual man is the probability of getting the woman he targets multiplied by the value of that woman. If the blonde knows her value, she should set her price at a level that makes her more attractive than a brunette for the man with the most “purchasing power”. Then the market will tend to an equilibrium where that is the man who goes after the blonde and everyone else goes after a brunette.

So, without any cooperation, we should end up with people paired off who have relatively the same value. The women with the lowest attractiveness are not getting messaged either because the low-value men believe they will be happier single or because the price signals are distorted at that end of the market. The women with the highest attractiveness are not getting messaged as much as their slightly-less-attractive competition because men perceive their price as being too high (either because the women are acting irrationally or because the price signalling is noisy).