Editing Talk:182: Nash

This page could do with rigor. "Could do" does not mean "needs", however. It is not incomplete, just a bit threadbare. --[[User:Quicksilver|Quicksilver]] ([[User talk: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? --[[User:Quicksilver|Quicksilver]] ([[User talk: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. [[User:Danshoham|Mountain Hikes]] ([[User talk:Danshoham|talk]]) 18:42, 19 September 2015 (UTC)

That misuse of "moot" irks me.
@@ Line 7: / Line 7: @@
 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. [[User:Danshoham|Mountain Hikes]] ([[User talk:Danshoham|talk]]) 18:42, 19 September 2015 (UTC)
-That misuse of "moot" irks me.{{unsigned|Flewk}}
+That misuse of "moot" irks me.
-Might "all three left with one guy" possibly be a reference to nuclear fusion, I wonder? It'd be up Feynman's alley, no doubt?[[Special:Contributions/162.158.162.193|162.158.162.193]] 16:34, 20 November 2023 (UTC)
-:Foursome night? [[User:42.book.addict|42.book.addict]] ([[User talk:42.book.addict|talk]]) 22:03, 2 February 2024 (UTC)