A Beautiful Mind - Nash equilibria vs Adam Smith's theory !

[MrKim218]

John Nash..!!

[xxXXSAWAMURAXXxx]

idol! 

[Gizmou07]

This is not Nash equilibrium! lol

[centurion180ad]

Bogus, a total misuse of Doctor Adam Smith's theory.

….not to mention that it’s a shorty of the 5 ladies, the long thick curly hair brunette in the navy & maroon skirt that is #1 sexy!

The object here is to go along with the others and //say// that the blonde is #1 and allow the peer pressure to leave the one that is the best mate wide open! Then play it up that you lost, when you walk away with the best lady without a struggle.

[ranganbd]

Studying base frame and differential frame for video streaming and this theorem come out :SSB (Slot Sell and Buy) scheduling policy achieves 100% throughput both in isolated input-queued switches and in networks of input-queued switches.

Watching movie sometime useful :D

[DKH1103]

The Nash Equilibrium is a set of strategies (one for each player), where no individual can improve by switching to a different strategy. In some situations there can be more than one equilibrium point, and that is the case in this example. A Nash Equilibrium here is any situation where just one man defects on his pals and goes for the blond, and everyone else goes for brunettes. If someone suspects that one of the group might defect, they can't improve by also defecting.

[screamsinfamous]

whats the song?

[Verradonairun]

If I understand the equilibrium correctly. There are many scenarios of competition where it does not apply, am I correct? No unqualified need reply.

[1tarekwaleed]

@Verradonairun Correct, Nash equilibrium does not apply in all situations.

[banzaofking]

I think the director doesn't know Nash equilibrium well

[HSWRKUHHUJHU]

thts the only way we all get laid 1:54

[Jackies1979]

it is also easy to see from my list of N.E. for *pure* strategies the nash equilibrium for *mixed* strategies which is also the justest one from a "social optimum" standpoint: each player takes with 0.25 probability blond, with 0.75 probability brunette....

[02hequba]

@Jackies1979 I am confused. Because of the condition of "nobody wants to be second choice", I think that no matter what choice every boy has, it will lead to a NE. So (bl, bl , br, br), for example, will still be a NE. But the social optimum (which indeed is a NE) will be that one chooses the blond and the others choose brunettes.

[Jackies1979]

@02hequba 1. a nash equilibrium is not always or necessarily a pareto optimum, in the case of the prisoner's dilemma, the nash-equilibrium is not pareto optimal... in this case, by accident, all the nash equilibria are also pareto-efficient 2. (bl, bl, br, br) meaning (0, 0, 3, 3) cannot be a nash equilibrium because, e.g., player 1 could change his strategy alone (not meaning actually switching from a bl to a br, but taking br in the 1st place) and get more: (br, bl, br, br) i.e. (3, 5, 3, 3)

[Jackies1979]

@Jackies1979 and to give the definition of a N.E. also: it is just this: a combination (or: "tuple") of strategies such that no player can increase his payoff by changing his own strategy alone.

[Jackies1979]

I now list all the nash equilibria for pure strategies of this game: (bl, br, br, br), (br, bl, br, br), (br, br, bl, br), (br, br, br, bl).

[Jackies1979]

@Jackies1979 interestingly, these 4 nash equilibria are incidentally also all pareto-efficient, so in a way they also all constitute something like "social optima", so there can be no difference between "social optimum" (at least in the sense of pareto-efficiency) and nash equilibria at all here -- contrary to the difference 02hequba claimed...!

[Jackies1979]

@Jackies1979 pareto-efficient meaning: it is impossible to increase the payoff of one player (by switching between strategies in any way) without decreasing that of some other player.

[02hequba]

2)The movie is more complex. It talks about the price of anarchy .The price of anarchy (PoA) is a measure of how well people do when they play selfishly (Nash equilibrium -everybody goes for the blond) versus choosing the social optimum (one goes for the blond and the other for brunettes). The case were they all go for brunettes is a NE, but it is not a social optimum.

[Jackies1979]

@02hequba @ 2) everyone going for the blond is not a nash equilibrium because -- as stated in the conditions (I as an "only twosomes okay" critic don't see why) -- two or more going for one person "block each other", and they get, say, 0 utility units: e.g. (br, br, bl, bl) is assigned to (3, 3, 0, 0) (they cannot then switch to brunettes, because -- I remember very well, no one "wants to be 2nd choice"). even worse: *all* take blond would mean (0, 0, 0, 0).

[Jackies1979]

@Jackies1979 so it is easy to see that every single player by switching his own strategy (from take blond to take brunette) can increase his payoff!! I am not talking about switching in the sense of trying to get the blond and then trying to get a brunette, I am talking about switching in the sense of taking brunette in the first place instead of blond in the first place... so all going for blond is *by no means* a Nash equilibrium, indeed nothing could be farther from it...

[kct53]

Verradonairun I'm sorry but you are incorrect and frankiedetorie is right. The Nash equilibrium states that by changing you strategy you will not be able to benefit yourself. In this example it's not true. One of the guys could easily change his strategy and ditch the brunettes for the absolutely gorgeous blond women. There the Nash equilibrium does not stand.

[pianetapda]

they just dont wanna getting laid, they dont care about the hot or not girl.

so if they f***k there's no incentive to change.

it's also about cooperation, or collusion: they could have somewhere a better payoff, but when they reach, cooperating, a "good" payoff they wont change it (remember, instead they could getting laid, so no incentive to change at eq).

[Jackies1979]

@kct53 yes, i mostly agree, though the example is not only bad because it simply is no nash-equilibrium that "nash" gives here but also because of the horrendous sexism of the game ;) frankiedetorie is right in saying that there is something wrong with the example here but I don't agree that Nash equilibrium "is almost always against the best collective outcome"... this may be true for the prisoners' dilemma, but it certainly is wrong for a battle of the sexes or stag hunt game situation...

[Jackies1979]

@Jackies1979 so you cannot say in general, frankiedetorie, that going for the blond is recommended by the nash equilibrium principle.... nash equilibria are constellations or tuples of strategies, and here the equilibria are such that no universal recommendation for the players is possible... however, it is very true that all the constellations in which all but one player (who goes for the blond) going for brunettes are all nash equilibria for pure strategies here...

[02hequba]

@Jackies1979 1)After they made their first choice (each one chooses a brunette ), it is not better for them to swich to the blond, because the blond will refuse them ("nobody wants to be a second choice", remember?).

[Jackies1979]

@02hequba I am not talking about "switching" to blond in the sense of actually trying to get the brunette and then trying to get the blond, i am talking about the definition of the N.E. "Switching" here need not actually take place!! Say getting the blond is 5 utility units, brunette 3, nobody 0. Now (br, br, br, br) with (3, 3, 3, 3) is simply defeated by (br, br, br, bl) with (3, 3, 3, 5) *without* player 4 having to *actually* switch from brown to blond!!! So blond is not 2nd choice!

[Verradonairun]

I have difficulties seeing the relation between the Nash equilibrium and this situation, as presented in the movie.

[ChronoZero]

Because the example in the movie is wrong :P It's not a nash equilibrium per se, as they will have incentives to switch to the blond at any time

[frankiedetorie]

Nash Equilbrium (unexploitable strategy) is to go for the blonde.

However the optimal solution for everyone is to go for the others. But this is exploitable.

[Verradonairun]

NO! don't ever say that, it'll make you sound stupid.

Nash equilibrium refers to the set of strategies in a given situation that guarantees the best COLLECTIVE outcome.

You are mistaking Adam Smith for Nash.

[frankiedetorie]

Wrong. Nash equilibrium is all about making unbeatable (unexploitable) plays.

Nash equilibrium is almost always against the best collective outcome.

For example in the prisoners game (if you do know it then your opinion is seriously degraded) the equilibrium strategy is the direct opposite of the optimal collective strategy.

Nash in the flim realised that the equilibrium strategy is not the the best collective strategy.

Work as a team? Collectively optimal

Go it along? Unexploitable

[turtlebelle]

A diet of the mind is not to over indulge in appetites of the mind !

[rikkieboy11]

What's the song played?

[TianAlex]

Dr. Nash!!! Brilliant Mind!!!