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

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10 sats \ 11 replies \ @SimpleStacker OP 3 Dec \ parent \ on: [Economics Puzzle] John Nash was wrong? econ

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.

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.