 Após o sucesso do filme Uma Mente Brilhante (A Beautiful Mind, em 2001), ganhador do Oscar 2002, que retrata a vida do genial John Nash interpretado por Russel Crowe, muitas pessoas usam a cena do bar como um exemplo de Teoria dos Jogos e Equilibrio de Nash.
O filme é realmente muito bom e a cena é fantástica. Você pode ver no YouTube neste link. Abaixo a reprodução (em inglês) da fala exata dos personagens no momento em que Nash e seus amigos vêem a loira e suas amigas morenas entrarem no bar. A principal frase está em destaque.
|  Nash: Oh. Does anyone else feel she should be moving in slow motion?
Bender: Will she want a large wedding, you think?
Saul: Shall we say swords, gentlemen? Pistols at dawn?
Hansen: Have you remembered nothing? Recall the lessons of Adam Smith, the father of modern economics.
Saul: Yes, in competition...
Group: ...individual ambition serves the common good.
Hansen: Exactly.
Nielssen: Every man for himself, gentlemen.
Bender: And those who strike out are stuck with their friends.
Hansen: I’m not gonna strike out.
Saul: You can lead a blonde to water, but you can’t make her drink.
Hansen: Uh, I don’t think he said that.
Saul: All right, nobody move. She’s looking over here. All right, she’s looking at Nash.
Hansen: Oh, God. All right, he may have the upper hand now, but wait until he opens his mouth. Remember the last time?
Bender: Ah yes, that was one for the history books.
Nash: Adam Smith needs revision.
Hansen: What are you talking about?
Nash: If we all go for the blonde, we block each other, and not a single one of us is going to 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. But 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? Incomplete. Incomplete! Because the best result would come from everyone in the group doing what’s best for himself and the group.
Hansen: Nash, if this is some way for you to get the blonde on your own, you can go to Hell.
Nash: Governing dynamics, gentlemen... governing dynamics. Adam smith was wrong. |
 Traduzindo a explicação de Nash:
. Se todos nós escolhermos a loira, nós vamos nos bloquear e nenhum de nós vai conquistá-la.
. Então partimos para as morenas, mas elas vão nos rejeitar pois ninguém gosta de ser a segunda opção.
. Mas e se ninguém for atrás da loira?
. Daí não competiremos entre nós e não insultaremos as amigas. Essa é a única forma de vencer.
A repercussão
Após o filme muitos se interessaram pela vida de Nash e suas idéias sobre Teoria dos Jogos. E imediatamente os especialistas e professores no assunto rebateram dizendo que, embora o filme seja genial, os fundamentos teóricos eram imprecisos. De fato, Hollywood quis retratar a biografia de Nash e sua esquizofrenia, e não dar aula sobre Teoria dos Jogos.
No DVD "Games People Play: Games Theory in Life, Business, and Beyond", o professor Scott P. Stevens comenta "So putting Hollywood on notice, you can mess with Nash´s life, but don´t mess with his equilibrium".
Abaixo dois links de pessoas provando que a solução do filme não é tecnicamente um Equilíbrio de Nash.
1. Site Mind Your Decisions - Artigo "Game Theory scene from A Beautiful Mind".
The movie is directed so well that it sounds persuasive. But it’s sadly incomplete. It misses the essence of non-cooperative game theory. A Nash equilibrium is a state where no one person can improve, given what others are doing. This means you are picking the best possible action in response to others—the formal term is you are picking a best response. (For more, see my article on why Nash equilibrium exist).
As an example, let’s analyze whether everyone going for a brunette is a Nash equilibrium. You are given that your three of your friends go for brunettes. What is your best response?
You can either go for the brunette or the blonde. With your friends already going for brunettes, you have no competition to go for the blonde. The answer is clear that you would talk to the blonde. That’s your best response. Incidentally, this is a Nash equilibrium. You are happy, and your friends cannot do better. If your friends try to talk to the blonde, they end up with nothing and give up talking to a brunette. So you see, when Nash told his friends to go for the brunettes in the movie, it really does sound like he was leaving the blonde for himself.
Now, in practical matters it will be hard to achieve the equilibrium that only one person goes for a blonde. There is going to be competition and someone in the group will surely sabotage the mission. So there are two ways you might go about it using strategies outside the game. One is to ignore the current group and wait for another group of blondes (the classic “wait and see” strategy). The second is to let a random group member go for the blonde as the others distract the brunettes (also practiced as “wingman theory”).
2. Universidade da Virginia, Departamento de Economia - Paper "A Beautiful Blonde: a Nash coordination game".
Dois professores escreveram um paper de 12 páginas com sofisticada matemática para mostrar que a solução é uma "mixed strategy".
Conclusão
É verdade que a cena do filme não pode ser usada de forma didática para explicar nenhum conceito técnico de equilíbrio e estratégia de Teoria dos Jogos. Mas serve para mostrar que a essência da Teoria dos Jogos é prever quais as decisões os demais jogadores (os amigos de Nash e as garotas) tomarão para assim ajustar a sua escolha. É o jogo de antever as ações e tomar a melhor decisão sabendo que os competidores estão pensando da mesma forma. Além disso, o filme é ótimo. |
