# How to get that blonde in a Bar?

Economists are fascinated by social interactions. And there is nothing more satisfying than being able to predict outcomes of such behavioral interactions.

Recall the last time you went to a bar. You are sitting with your mates when a group of beautiful ladies walk in. All but one of them, brunettes. You are immediately drawn towards the Blonde, but just as you are about to go and chat her up, you realize your mates are thinking the same.

In a situtation, right out of the movie "A Beautiful mind", you have a couple of options. You can either disregard your competition, and try to reach her first. But failing would also mean losing the chance to go home with the Brunettes, who hate to be the second choice. Also, if all of you make a move towards the Blonde, it's sure to scare her off and everyone ends up going home alone.

Alternatively, you and your mates could collectively decide not to go for the Blonde, and approach the Brunettes. Lastly, just one goes for the blonde, whereas the rest go for the Brunette. So which is the best strategy?

Game theory gives the players solid recommendations on their optimal strategy and provides an external observer with a prediction of the outcome of the interaction.

Now, let's evaluate. First choice is right out of Adam Smith's book, "in competition, individual ambition serves the common good". This lesson of the father of modern economics suggests that it would be best for the group if all the boys go for the blonde girl.

In the movie, Nash's character argues that the above theory needs a revision and in fact the best strategy is everyone going for the Brunette since it ensures no one goes home alone.

Now let's apply game theory into it. Strategy 2 is a good strategy since the group is collectively better off than going home alone (Strategy 1). However it is not Pareto Optimal. Any guy could be made better off by going for the Blonde, without making someone else (in his group) worse off, which brings us to the last strategy -one for the blonde and rest for the brunettes.

So how does the game end? Who goes with the Blonde? Who do "you" go home with? Do you go home alone?

Let's put all the pieces together. Nash, in the movie suggests stratergy 2, with all implicit intentions of just himself going for the blonde, which clearly is the group-optimal (Pareto) strategy.

If all your mates are economists and have similar personalities, toss a coin to decide who goes after the blonde. Economists have great personal integrity ;)

In real life, however, the prediction also relies a lot on other factors. Since it is a co-operative strategy agreed with your mates, we have excluded external suitors. Say if Brad Pitt (or someone more attractive than your group), is drinking in the same bar. Then just go for the Brunette, since Brad Pitt always gets the blonde (infact all the blondes).

To sum up, you get the blonde if and only if,

- There is no Brad Pitt in the same bar eyeing for the blonde and,

- You won the toss and your mates decide to back off

Happy Pubbing..

PS: The above sterotyping women based on their hair color was purely to illustrate a point. I personally prefer Brunettes and wouldn't have gone for the blonde :)

Sources:

http://plus.maths.org/content/if-we-all-go-blonde