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April 24, 2009

Beautiful, but Hollywoodized mind

All economists have followed the story of John Nash as he recovered from 35+ years of paranoid schizophrenia in the mid 1990s, and was awarded the Nobel Prize for his Ph.D. dissertation in which he invented the core concepts of non-cooperative game theory. After all, every last one of us learned Nash equilibrium in our first year of graduate school (or earlier), and an awful lot of us use the concept daily in our research and teaching.

And so, like many others, I read Sylvia Nasar's biography A Beautiful Mind as soon as it came out. Then rushed to see the Russell Crowe movie by the same name.

Oh no! In the key scene of the movie (well, to us economists), when Nash excitedly explains his equilibrium concept to his buddies while sitting in a bar...the screenwriters got it wrong. The "Nash equilibrium" Crowe describes in fact is not an equilibrium. Not even close: every one of the three players in the game described has an incentive to deviate and go for the blonde. Grave disappointment. How could Hollywood spend many millions on a biography of a game theorist, and get his most famous, and let's face it, rather straightforward concept wrong?

Over the years, when I would teach introductory game theory to students, I usually mentioned the popular movie to motivate them a bit, and quickly sketched the highlights of Nash's strange life. Then I would say "but the Nash equilibrium in the bar scene is wrong" and let them figure it out as an exercise. (Easy in recent years, since they can go find the clip on YouTube.)

Of course, most anyone who knows a bit of game theory and saw the movie surely spotted the mistake: it's a bonehead error. But just today I discovered that his mistake has really made it in pop culture: it's the punch line of an xkcd comic (http://xkcd.com/182/)!

(Thanks to Jon Kleinberg via Chuck Severance for leading me to this gem.)

Posted by jmm at April 24, 2009 12:11 AM

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