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0 sats \ 2 replies \ @SimpleStacker OP 3 Dec 2024 \ parent \ on: [Economics Puzzle] John Nash was wrong? econ
This is correct enough. In the end, they will randomize. To be fully exhaustive, there are actually C_3^4 + C_2^4 + C_1^4 + 1 Nash equilibria!
  • C_3^4. Three of the guys go for the blonde's friends, one guy goes for the blonde.
  • C_2^4. Two of the guys go for the blonde's friends. Two of the guys randomize over the blonde.
  • C_1^4. One of the guys goes for the blonde's friends. Three of the guys randomize over the blonde.
  • 1. 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 2024
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 2024
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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