Yesterday I taught the first of five algorithmic economics lectures in my undergraduate AI course. This lecture just introduced the basic concepts of game theory, focusing on Nash equilibria. I was contemplating various ways of making the lecture more lively, and it occurred to me that I could stand on the shoulders of giants. Indeed, didn’t Russell Crowe already explain Nash’s ideas in A Beautiful Mind, complete with a 1940’s-style male chauvinistic example?
The first and last time I watched the movie was when it was released in 2001. Back then I was an undergrad freshman, working for 20+ hours a week on the programming exercises of Hebrew U’s Intro to CS course, which was taught by some guy called Noam Nisan. I didn’t know anything about game theory, and Crowe’s explanation made a lot of sense at the time.
I easily found the relevant scene on youtube. In the scene, Nash’s friends are trying to figure out how to seduce a beautiful blonde and her less beautiful friends. Then Nash/Crowe has an epiphany. The hubbub of the seedy Princeton bar is drowned by inspirational music, as Nash announces:
If we all go for the blonde, we block each other. Not a single one of us is gonna get her. So then we go for her friends, but then they give us the cold shoulder because nobody likes to be second choice. Well, what if no one goes for the blonde? We don’t get in each other’s way, and we don’t insult the other girls. That’s the only way we win. … Adam Smith said the best result comes from everyone in the group doing what’s best for himself, right? … The best result would come from everyone in the group doing what’s best for himself and the group!
But if no one goes for the blonde, wouldn’t a player gain from deviating to the blonde, without making others worse off? This game has Pareto efficient Nash equilibria (one player goes for the blonde, the others go for her friends), but the strategy profile advocated by Crowe is not Pareto efficient, nor an equilibrium.
Nash concludes by proclaiming “Adam Smith was wrong!” Maybe, but so was Russell Crowe.