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08 May How to use mathematics for love

Mathematician John Forbes Nash knew how to get the right girl.Mathematician John Forbes Nash knew how to get the right girl.

If you walk into our Faculty of Science as an outsider (a non-geek) you might think that everyone in the library is all about studying and that their heads are only full of formulas and numbers. But we geeks know better. Just like other young people we spend a considerable amount of time thinking about love and sex. About how to get the right girl, or how to get that boy for one night. If you still don’t believe this, spend a night at one of the parties of a student association, you will see. You might also see some strange things; the most beautiful girls are left out! This is not because geeks have different taste, but because they use mathematics. Learn from the story of the great mathematician John Forbes Nash.

A physic’s party
You might know Nash from the movie A Beautiful Mind. This amazing movie is about the troubled life of Nash, about his genius and schizophrenia .  The genius mathematician came up with what we now call the Nash-equilibrium. This turned out to be such an important concept in economy, that Nash won the Nobel Prize in 1994. But how can Nash help you get the girl?
Let us imagine being at a party of NSA, the student association of physics and mathematics students.
Four male physics freshmen are at the party, drinking beer and looking for some girls. Five girls walk in, slightly older mathematic seniors. They all look amazing, but one really stands out, the girl with the glasses!  The guys get a little nervous, and start to think what is the best strategy to approach the girls.

Choosing for yourself is not always the best option
Economist Adam Smith would say, best result comes from everyone in the group doing what is best for themselves. Now what Nash found out is that game-theoretically this is not always right. Because imagine the guys would do what is best for themselves, and all move slowly towards the girl with the glasses; offer her a drink, put their hands on her hip or whisper in her ear. The girl will think, it is always the same with these freshmen, leave me alone. And after she gave the four guys the blues, they will go for the other girls. But since no one likes to be second choice, at the end of the evening, they will all go home alone. Result zero!

Cooperating strategy
What Nash thought of was that a better result will come from a cooperating strategy. Because what if no one went for the girl with the glasses? The freshmen can all go for a nice girl and the only one who goes home alone is the girl with the glasses. Result: four happy freshmen. This is what Nash finds out in the movie (unfortunately, after he thought of this, he goes home alone to work out his theory), but if we look into the theory, the situation is not exactly a Nash Equilibrium.

A Nash Equilibrium
Informally, a Nash Equilibrium is described as a set of strategies in which no one can do better by changing his strategy. In the case of the NSA party, this is not exactly the case. If only one guy decides to change his strategy and go for the glasses girl instead of one of the others, he will do better. So one guy should go for the glasses girl to reach a Nash Equilibrium. Because then no one would consider changing his strategy to do better. But who should this be? Another Nobel Prize winner answers this question; Thomas Schelling. He proved that some game-theoretical strategies arise naturally.

Spontaneous Equilibrium
Imagine there are two people, unable to communicate, having to select one out of four squares, without the other one knowing. If they both choose the same one, they win a prize. Three of the squares are blue, one is red. Probably, they will both choose the red one. Not because the red one is better  but the strategy appears to be the natural right strategy. The same happens with a Nash equilibrium, it can emerge spontaneously, in a self-evident way.
So back to the party, the situation can naturally emerge into a Nash equilibrium. For example, because the slightly better looking guy, who has more experience with women, dares to go for the beautiful girl with the glasses, and gets her. The other guys will naturally let him, because they know that it is in their best interest to go for another girl.
So what we can learn from the great Nash, is that being too selfish is not going to get you laid. Go for the cooperate strategy! But also think of Schelling, and accept that your good looking friend just naturally causes the equilibrium. Blame it to science!

Watch the famous scene from A Beautiful Mind here.  Or better, watch the whole movie! What do you think of the movie? Is Nash right or do you use other strategies? Tell me in the comments!

WTFmarie beth

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