[Economics Puzzle] John Nash was wrong? \ stacker news ~econ

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625 sats \ 26 comments \ @SimpleStacker 3 Dec econ

Watch the bar scene from the movie, A Beautiful Mind.

In the scene, a beautiful blonde walks into a bar with four of her less attractive friends. Four male grad students begin competing with each other for the blonde's attention. They justify the virtue of competition with Adam Smith's words, "Individual ambition serves the greater good."

This causes Nash to have a revelation. "Adam Smith needs a revision," he says, explaining:

If we all go for the blonde, we block each other. She won't choose any of us. If we then go for her friends, we'll likewise get rejected because no one wants to be second choice.
But if no one goes for the blonde, we don't get in each others' way and we don't insult the other girls. That's the only way we win. The only way we all get laid.

First person who can correctly explain why this movie version of John Nash was actually wrong, gets 1,430 sats.

I think out of fairness, I would ask @Undisciplined and @denlillaapan to refrain from answering unless no one has gotten it in a few hours, since both appear to have formal training in economics :)

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12 replies \ @Imyourfed 3 Dec

The movie’s strategy isn’t a Nash Equilibrium because it’s unstable. If everyone ignores the blonde, one guy has an incentive to go for her, disrupting the plan. A Nash Equilibrium requires no incentive to deviate, which isn’t the case here.

10 sats \ 11 replies \ @SimpleStacker OP 3 Dec

Ok, this is the first complete answer, but @Arceris also came close :)

Now, I'll pay a second bounty to anyone who can tell me what the actual Nash equilibrium is

30 sats \ 6 replies \ @south_korea_ln 3 Dec

Every one decides for himself if they have better luck at going for the blonde or going for the other girls. No cooperation should be required. For some, due to their own attractiveness, they know that they likely have a higher change at the blonde so they might opt for this option, while if you are slightly above average, you might think it's better to forget about that small edge and simply go for the other girls. Optimize by comparing your odds with the odds of the others.

0 sats \ 4 replies \ @SimpleStacker OP 3 Dec

Close, but not quite correct in terms of a Nash equilibrium.

Because if two of the males had, say, equal attractiveness, and both decided to go for the blonde, they'd block each other and it wouldn't be Nash. One of them would be better off going for the brunette first, rather than blocking each other.

1430 sats \ 3 replies \ @south_korea_ln 3 Dec

Close, but not quite correct in terms of a Nash equilibrium. Because if two of the males had, say, equal attractiveness, and both decided to go for the blonde, they'd block each other and it wouldn't be Nash. One of them would be better off going for the brunette first, rather than blocking each other.

So one should consider a choice based on one's probability of being successful rather than have a fixed and definite choice? Using these odds, sometimes going for the blonde, sometimes not. This should resolve the problem if two males have an equal level of attractiveness, no?

0 sats \ 2 replies \ @SimpleStacker OP 3 Dec

This is correct enough. In the end, they will randomize. To be fully exhaustive, there are actually

Nash equilibria!

. Three of the guys go for the blonde's friends, one guy goes for the blonde.
. Two of the guys go for the blonde's friends. Two of the guys randomize over the blonde.
. One of the guys goes for the blonde's friends. Three of the guys randomize over the blonde.
. All of the guys randomize over the blonde.

The exact probabilities in each equilibrium depend on the relative utilities of the blonde, her friends, and getting no one.

30 sats \ 1 reply \ @south_korea_ln 3 Dec

Thanks for formalizing it and hinting me in the right direction. And thanks for the sats :)

EDIT: so, (4+6+4+1=)15 equilibria?

119 sats \ 0 replies \ @SimpleStacker OP 3 Dec

so, (4+6+4+1=)15 equilibria?

That should be correct, assuming all the males are actually identical. If they have different preferences, or if the blonde may select one over another when there's a conflict, then the solutions could change.

Fun fact: The number of Nash equilibria, including randomized ones, which we call "mixed strategies", is always odd.

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0 sats \ 0 replies \ @south_korea_ln 3 Dec

Now, if Nash's odds are increased by convincing the others about the validity of his Nash equilibrium scenario, and he still goes for the blonde himself, this would not be cooperation but deceit. If he knows his friends are stupid to fall for it, seems like a good equilibrium after all.

EDIT: I should go watch the clip, I don't remember the details of what actually happened.

0 sats \ 3 replies \ @Imyourfed 3 Dec

deleted by author

30 sats \ 2 replies \ @Imyourfed 3 Dec

Damn! I messed up a little on explanation lol

But it was fun!

41 sats \ 1 reply \ @SimpleStacker OP 3 Dec

I hope to post more econ and game theory based puzzles :)

0 sats \ 0 replies \ @Imyourfed 3 Dec

Sure :)

I'm discovering a lot more here and your puzzles will be amazing!

227 sats \ 1 reply \ @Arceris 3 Dec

Nice hook, but the Real Nash isn’t wrong 🤣

I, however, may be (and I probably am) wrong.

But I believe the formal design of a nash equilibrium doesn’t require coordination between the actors, whereas the movie version seems to imply that the men need to cooperate (in a kind of prisoner’s dilemma).

A Nash equilibrium, if i recall correctly, results in an optimal strategy for each actor regardless of the actions of other actors, and no actor can improve their outcome without cooperation.

26 sats \ 0 replies \ @Undisciplined 3 Dec

no actor can improve their outcome without cooperation

Yep. No unilateral improvements is one of the requirements.

15 sats \ 1 reply \ @Undisciplined 3 Dec

Are we allowed to provide intentionally stupid answers?

30 sats \ 0 replies \ @SimpleStacker OP 3 Dec

Go for it, I might even reward some sats for fun ones :)

1440 sats \ 3 replies \ @Undisciplined 3 Dec

He shouldn't have assumed that she wouldn't take all nine of them home.

44 sats \ 1 reply \ @denlillaapan 21h

slut

0 sats \ 0 replies \ @Undisciplined 19h

No risk it, no biscuit.

28 sats \ 0 replies \ @SimpleStacker OP 3 Dec

In economics, it's always wise to question your assumptions

30 sats \ 2 replies \ @TheMorningStar 3 Dec

Thanks. Not looking for reward but please tell me if it's the correct explanation of Nash theory?

Nash equilibrium, in game theory, an outcome in a noncooperative game for two or more players in which no player's expected outcome can be improved by changing one's own strategy.

10 sats \ 1 reply \ @SimpleStacker OP 3 Dec

Yes, that's correct. In a Nash equilibrium, no one player can improve their outcome by unilaterally changing their own strategy.

0 sats \ 0 replies \ @TheMorningStar 3 Dec

Thank you for some new learning.

0 sats \ 0 replies \ @denlillaapan 21h

Well, that wouldn't help me. I remember having had this problem in game theory class -- doesn't mean I remember the solution, haha. Probably something to do with unstable eq or non-credible promises, cartel style

0 sats \ 0 replies \ @MaaliMKen 3 Dec

The economist looking at the group is also a factor we need to consider.