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1430 sats \ 3 replies \ @south_korea_ln 3 Dec \ parent \ on: [Economics Puzzle] John Nash was wrong? econ
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?
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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.
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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?
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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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