Nash's Equilibrium

[RicRagsLive]

Ok wait, I still kinda wanna hump the blonde.

[Armin600]

if Adam Smith said, "the best result comes from everyone in the group doing what is best for themselves" then Smith is WRONG because for eg in a 3 player game, if everyone cheats ( i.e. DOES what is indeed best for themselves) then the total group's payoff declines substantially and of course the greater the number of players the greater the magnitude of the incentive to cheat becomes - so THAT part of the movie is right.

[johnson161]

the scene reminds me of the american psycho scene about girls. look at 0:28 and compare. josh lucas is in both of them.

[Mavrick369]

The last person to move would go for the blond, while those who moved before would go for the brunettes.

[dbullet]

Actually I just read through some comments and realized this had already been discussed to death... I got all excited after I figured out that the movie got it wrong! lol ))) The movie treats the game as if it is a coordination problem, when it is actually a prisoner's dilemma...

[dbullet]

Uhm.... my contention is that the solution proposed by Russel Crowe is actually NOT a Nash equilibrium. In this outcome, each player can unilaterally improve his payoff by going for the blonde, assuming the rest of the group goes for the brunettes. The Nash equilibrium is actually the "bad" outcome he initially proposes! Maybe someone mentioned this though... did not read through comments...

[wvbuchem]

Where can i find the music of this clip? This piece of music isn't on the soundtrack cd...

[MrWoweeZowee]

Id get them all cause im a player

[LakerGirl2489]

I prefer Prisioner's Dilemma explanation based on the two prisioner example... I think it's easier to understand

[53Aubergine]

I was going through some of my father's books and found my grandfather's edition of Adam Smith's book. Before I saw this movie it was just another old book...

[ThisCanadian]

53Aubergine : you might wanna investigate PNAC, Smith's militarized devotees tinyurl com/4juvjh "To ravage, to slaughter, to usurp under false titles, they call empire; and where they make a Desolation, they call it Peace." - Calgacus, per Tacitus. There is no 'we' in corruption: tinyurl com/358qy4 IP Report "Resource Scarcity: Responding to the Security Challenge" tinyurl com/5xzr7v ┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄ BlueBerry Pick'n ThisCanadian com ┄┄ "We, two, form a Multitude" Ovid ┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄

[economicatheist]

porthouse: then clear up where I made a mistake. The movie does not just "oversimplify" the idea. It gets it completely wrong. Some guys in my department even have a working paper in which they point out the movie's error and then deduce all the real Nash equilibria.

[fusionjady]

What is the real nash equilibria? Im curious

[joshrob41942]

A Nash Equilibrium occurs when all players are playing their mutual best responses. In other words, each player does the best he can considering what the other players choose. In this scenario, if any player believed that all other players would go after the brunettes, then his best response would be to go after the blond (because the other players would no longer be "blocking" him). Thus, all players going after brunettes cannot be a Nash Equilibrium.

[joshrob41942]

Additionally, the paper in which Nash developed the idea that became known as "Nash Equilibrium" is entitled "Non-cooperative Games." As one might imagine, a non-cooperative game is one in which the players do not cooperate. Which means no player will consider the other players payoff when making his decision... i.e. the movie got the concept COMPLETELY wrong

[argumentiscreative]

Joshron1492, thanks for the explanation. Just out of curiousity, if the players are not cooperating who will they ever know whether all other strategies are worse than the one they have chosen - how can they ever be in equillibrium?

[joshrob41942]

The original concept of Nash Equilibrium was dependent on the idea that all players know each others payoffs. So while one player might not know how the other player is going to move, he knows his own payoff, which gives him a best response for each move, AND he know his opponents payoffs, so he can calculate his opponents best response to each of his moves. When both players are best responding to each other--the game has reached Nash equilibrium.

[joshrob41942]

To clarify this with my earlier comment, players consider others payoffs to anticipate their moves. But in a non-cooperative game any one player does not care how well-off the other players are in equilibrium. So they are not doing what is best for themselves "and the group". They are just doing what is best for themselves, by rationally anticipating what the group will do. There is a whole other branch of game theory in which player cooperate, but Nash did not explore this until later.

[vejamos]

All of this is quite interesting, but do you know that J. Nash did great things in geometry and partial differential equations???

[hacastro22]

You're forgetting something, in fact every single player in this game is tempted to betray their previous agreement. If more than one player betrays their group and goes after the blond, they'll end up blocking each other's way. So still, it is a Nash equilibrium to go after the brunettes.

The only way you could be right is if a player knew all the other players would go after the brunettes, so that he can chase the blond girl by himself.

[joshrob41942]

Not quite... You're making the right point, but coming to the wrong conclusion. A Nash equilibrium exists when all players are best responding (no incentive to deviate from their current strategies) to what the other players are ACTUALLY doing--not what they THINK they are doing. This is probably one of the hardest concepts for people to understand about game theory.

[joshrob41942]

Let's say you, "Bill", and I are playing this game. You have a strategy--I may not know it, but you have a strategy none the less. If you're strategy or Bill's strategy was to choose blonde, my best response would be to choose brunette. However, if you're strategy and Bill's strategy were to choose brunette, my best response would be to choose blonde. The Nash equilibrium is the set of strategies (not beliefs) in which no player would pick a different one--i.e one player picks blonde.

[joshrob41942]

The strong incentive to pick blonde (as you pointed out) is the reason why all players picking brunette cannot be a nash equilibrium.

[hacastro22]

Ohhh I see... so we're actually talking about strategies. But what about the "prisoner dilemma", where both prisoners do not know whether the other one will confess or not? Wouldn't the prisoners be thinking what the other will do? Or what about when companies decide to set their price based on what they think their competition will do?

I'm sorry, I was just studying microeconomics and I came across the Nash equilibrium :P I'd appreciate your answer so that I can better grasp this concept.Thanx!

[joshrob41942]

The belief is implicit in the equilibrium. If your strategy is part of the equilibrium then I must "believe" that you will do it. So in the prisoner's dilemma, one player "believe" the other will confess. Why? Because no matter what one player does the other players has dominant strategy to confess. Price setting is a little more complex (we have to know a lot about the relationship between the companies), but the idea is essentially the same. Your intuition is very good; I hope this helps

[hacastro22]

It sure did. Thank you! I'm still trying to fully understand the equilibrium in non cooperative games (wonder how it works with cooperative), but you just gave me a lift.

[dbullet]

You were right originally. Choosing the rat the other guy out in the Pris. Dil. is a purely dominated strategy. There is a series of lectures on game theory on Yale's open education youtube page... they also give some books to read. Great instructor, I highly recomend it.

[JackHonak]

Hello Josh, I found it really interesting the way you think and how you put things in perspective. Yet, what you are explaining is not pure and equation-based mathematics. My question could sound naive, but is there a recognized science of philosophical Math? And if there is, what books category should I be looking under? Or is it simply reading those equation in simple English? .. Thanks ..

[joshrob41942]

It's basically reading math in simple English. The nice thing about game theory is that, since it's about people's behavior, it's easy to describe in words. In fact, one can learn an extraordinary amount about the subject without every writing an equation. Most introductory textbooks on game theory will be written in this fashion.

[JackHonak]

Thanks.

[watermelonobserver]

@fusionjady the real nash equilibrium would be that everyone goes for the blonde, because the blonde is considered of greater value than the other girls, hence if each guy went for the other girls they would stand to gain by going for the blonde instead, right?

That would make the action of every guy going for the other girls the pareto optimum, not the nash equilibrium.

Technically the movie isn't wrong; it never said that the pareto optimum was the nash equilibrium.

[economicatheist]

Too bad the movie producers presented the American public with a false idea of a Nash Equilibrium (NE). The equilibrium where all men go for brunettes is not a NE. In fact, assuming that the men are indifferent between any two brunettes and that no man has the ability to always get the blonde (e.g. she likes Nash better), any equilibrium where all men get a girl and one man gets the blonde is a NE. Fun movie; dumb Hollywood.

[porthousevike07]

The movie does a great job of introducing the NE. It gives a basic, easy to understand idea behind it. It's quite oversimplified, but, it gives one an idea to think about. By the way, you are not completely correct either, but whatever.

[Congo4life]

they should've brought in Darwins "only the strong survive"

[KlaxonCow]

Not possible. Because Darwin never said that.

"It is not the strongest, nor the most intelligent, of a species that survives. It is the one most adaptable to change."

- Charles Darwin

[LETTIS79]

well, they are 5 guys. In the scene all nash's friends get's a brunett girl but who gets the blonde...? Well nash!

[EGarrett01]

Wow, excellent scene. I should re-watch this movie. Thanks!