#b#From the movie, ‘A Beautiful Mind,’ starring Russell Crowe:#/b#
Below is the dialogue from the bar scene in the movie, when John Nash and some of his fellow math students are all eying the blonde who just walked in:
John Nash: Does anyone else feel she should be moving in slow motion ?
Bender: Will she want a large wedding, ya think?
Sol: Shall we say swords, gentlemen? Pistols at dawn?
Hansen: Have you remembered nothing? Recall the lessons of Adam Smith, the father of modern economics.
Sol: “In competition…”
Sol and Neilson: “. . . individual ambition serves the common good.’’
Neilson: Every man for himself, gentlemen.
Bender: And those who strike out are stuck with her friends.
Hansen: I’m not gonna strike out.
Sol: You can lead a blonde to water, but you can’t make her drink.
Hansen: I don’t think he said that.
Sol: Nobody move. She’s looking over here. She’s looking at Nash.
Hansen: Oh, God. He may have the upper hand now, but wait until he opens his mouth. Remember the last time?
Bender: Oh, yes, that was one for the history books.
John Nash: Adam Smith needs revision.
Hansen: What are you talking about?
John Nash: 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 they will all 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. That’s the only way we all get laid. Adam Smith said the best result comes from everyone in the group doing what’s best for himself, right? That’s what he said, right?
John Nash: Incomplete. Incomplete, okay? Because the best result will come from everyone in the group doing what’s best for himself and the group.
#b#From the book, ‘A Beautiful Mind,’ by Sylvia Nasar:#/b#
In the summer of 1949 . . . John Nash and another student were buying beers for a crowd of graduate students and professors in the bar in the basement of the Nassau Inn — as tradition demanded of men who had just passed their generals. The mathematicians were growing more boisterous and drunken by the minute. A limerick competition was in full swing. The object was to invent the cleverest, dirtiest rhyme about a member of the Princeton mathematics department, preferably about one of the ones present, and shout it out at the top of one’s lungs. At one point a shaggy Scot aptly named Macbeth jumped to his feet, beer bottle in hand, and began to belt out stanza after stanza of a popular and salacious drinking song, with the others chiming in for the chorus: “I put my hand upon her breast/She said, ‘Young man, I like that best’/(chorus) Gosh, g’or, blimey, how ashamed I was.”
That night, with its quaint, masculine rite of passage, marked the effective end of Nash’s years as a student. He had been trapped in Princeton for an entire hot and sticky summer, forced to put aside the interesting problems he had been thinking about, to cram for the general examination . . .
Nash’s “wasted” summer, with its enforced break from his research, proved unexpectedly fruitful, allowing several vague hunches from the spring to crystallize and mature. That October, he started to experience a virtual storm of ideas. Among them was his brilliant insight into human behavior: the Nash equilibrium. . .
The entire edifice of game theory rests on two theorems: von Neumann’s min-max theorem of 1928 and Nash’s equilibrium theorem of 1950. . . Von Neumann’s theorem was the cornerstone of his theory of games of pure opposition, so-called two-person zero-sum games. But two-person zero-sum games have virtually no relevance to the real world. Even in war there is almost always something to be gained from cooperation. Nash introduced the distinction between cooperative and noncooperative games. Cooperative games are games in which players can make enforceable agreements with other players. In other words, as a group they can fully commit themselves to specific strategies. In contrast, in a noncooperative game, such collective commitment is impossible. There are no enforceable agreements. By broadening the theory to include games that involved a mix of cooperation and competition, Nash succeeded in opening the door to applications of game theory to economics, political science, sociology, and, ultimately, evolutionary biology.