# 182: Nash

Nash |

Title text: Maybe someday science will get over its giant collective crush on Richard Feynman. But I doubt it! |

## Explanation

The first panel references a scene in the movie A Beautiful Mind in which Dr. John Forbes Nash, Jr. comes up with his famous concept of Nash equilibrium when he realizes that they get suboptimal results if all the guys go after the same hot girl. The second panel deconstructs the idea as Dr. Nash point out that staying away from the hot girl does not actually constitute a stable Nash equilibrium. The third panel has physicist Dr. Richard Feynman render their entire discussion a moot point by getting all the girls while the mathematicians ponder optimal strategies.

In fact, the situation in the comic is a great example of what a Nash equilibrium is *not*. The only reason that one player (pun intended) wouldn't try to go for the hot girl is if they were afraid that someone else would go for the hot girl as well. However, in a Nash equilibrium, each player assumes that the other players won't change their strategy, and concludes from this assumption that their own strategy shouldn't change either. If all of them have the strategy of flirting with the hot girl's friends, and all of them are assuming (incorrectly) that the others won't change their strategies, then they all would change their strategies simultaneously, breaking the equilibrium.

Feynman shared the Nobel Prize in Physics in 1965 for his important work in quantum electrodynamics. Feynman wrote popular books and gave public lectures. These presented his work in advanced theoretical physics to the general public, a practice that was not very common at that time. One of his more famous books, *Surely You're Joking, Mr. Feynman!* gives many personal anecdotes from his lifetime, and it contains a passage giving advice on the best way to pick up a girl in a bar.

The aforementioned public books and lectures brought him great attention in the media, and his exceptional results in physics coupled with this have led to his getting an almost cult-like following among scientists. He's also (largely due to his book) known as something of a womanizer, thus why he would take several women home at once.

The title text explains that Randall wonders whether this "collective crush" (crush as in love affair) will fade away one day, but he doubts it. Great respect for Feynman continues to this day, even though he died about a quarter-century ago.

## Transcript

- [Cueball and Dr. Nash (the Cueball-like guy to the right) stand talking to each other. Cueball is looking left and pointing off-panel.]
- Cueball: Hey, Dr. Nash, I think those gals over there are eyeing us. This is like your Nash Equilibrium, right? One of them is hot, but we should each flirt with one of her less-desirable friends. Otherwise we risk coming on too strong to the hot one and just driving the group off.

- [Cueball is now looking at Dr. Nash.]
- Dr. Nash: Well, that's not really the sort of situation I wrote about. Once we're with the ugly ones, there's no incentive for one of us not to try to switch to the hot one. It's not a stable equilibrium.

- [Cueball again looks left while Dr. Nash shakes his fist.]
- Cueball: Crap, forget it. Looks like all three are leaving with one guy.
- Dr. Nash: Dammit, Feynman!

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# Discussion

This page could do with rigor. "Could do" does not mean "needs", however. It is not incomplete, just a bit threadbare. --Quicksilver (talk) 05:27, 24 August 2013 (UTC)

Argh! How "wrong" was the title text, anyway? What remains to be explained, or what is incorrect? --Quicksilver (talk) 04:24, 25 August 2013 (UTC)

Explaining the Nash Equilibrium in the context of picking girls at a bar (as shown in the Beautiful Mind movie): The underlying mathematical assumption is that going home with any girl is superior to going home alone, and going home with the hot girl is superior to going home with an ugly one. Furthermore, each girl can only go home with one guy and each guy can only take one girl (an assumption that is humorously violated in the third panel). Under this system, if all guys were to approach only the hot girl, only one (at best) will take her home, and the rest will go home alone. A superior strategy would be for just one guy to approach the hot girl, and for the rest to approach the ugly ones. That way, everyone gets to go home with some girl. The core question is if this is a stable arrangement. If even one party benefits from violating the arrangement -- for example by ditching the ugly girl assigned to them under the arrangement and competing for the hot one -- the arrangement is not stable. If no one can benefit from violating the arrangement, then it is stable. Stable arrangements are referred to as "Nash Equilibriums." Whether a particular bar situation generates a Nash Equilibrium depends on the predictability of the hot girl's selection process when multiple suitors are available. If fully predictable, then an Equilibrium will exist (only the most qualified of the guys need approach the hot girl, anyone else doing so is futilely wasting their opportunity to take an ugly girl home). Of course, part of what makes a girl hot is unpredictable behavior (which causes multiple men to compete for her). If not very predictable, then its a matter of the relative benefit of the hot girl relative to the ugly ones versus the risk of going home alone. Mountain Hikes (talk) 18:42, 19 September 2015 (UTC)

That misuse of "moot" irks me. -- Flewk (talk) *(please sign your comments with ~~~~)*