In the film *A Beautiful Mind* about John Nash, there is a scene which purports to dramatize the moment in which Nash developed his idea for Nash equilibrium. He and three mathematician buddies are in a bar (here I might have already jumped to the conclusion that the story is bogus, but I just got back from Princeton and I can confirm that there is a bar there.) There are four brunettes and a blonde and the four mathematicians are scheming about who will go home with the blonde. Nash proposes that the solution to their problem is that none of them go for the blonde.

Let’s go to the video.

Of course this is not a Nash equilibrium (also it is inefficient so it cannot be a dramatization of Nash’s bargaining paper either.) However, this makes it the ideal teaching tool.

- This game has multiple equilibria with different distributional consequences.
- The characters talk before playing so its a good springboard for discussion of how pre-play communication should or should not lead to equilibrium.
- One of the other mathematicians actually reveals that he understands the game better than Nash does when he accuses Nash of trying to send them off course so that Nash can swoop in on the blonde.
- Showing what isn’t a Nash equilibrium is the best way to illustrate what it takes to be a Nash equilibrium.
- It has the requisite sex to make it fun for undergraduates.

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May 14, 2009 at 12:06 am

Joshua GansI think you’ll find that it is the Nash bargaining solution with non-transferable utility. That only requires Pareto efficiency which given that each man would supposedly have negative utility if another were to date the blonde and the preferences of all of the other women, is the outcome in the film.

May 14, 2009 at 9:35 am

MattCrowe Equilibrium: a strategy profile in which every player does strictly better by deviating given the strategies of others. Brilliant!

May 17, 2009 at 10:47 am

wcsInteresting, for movie, article and comment. But non-transferable and relative-state dependent utility is such a strong assumption.

May 31, 2009 at 6:25 pm

michael webster1. I agree that the Nash equilibrium never requires anymore than one person, in essence, to reflect on the problem to arrive at a calculation which will also perform the role of a solution or recommendation.

2. But, I disagree with the view that this is a good video for motivating the attraction of the Nash calculation. On the contrary, the clear instability of the recommended solution, which is nonetheless attractive, speaks volumes against the Nash calculation.