Re: Game Theory and Poker
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Just a minor whinge. I am not sure that the description of Nash Equilibrium is wrong in "A Beautiful Mind"? Isn't Nash supposing that if anyone were to alter their strategy and go for the Blonde then that would cause the others to similarly alter their strategy? Thus they are optimal if they stick with their own brunette! It's a kind of Prisoner's Dilemma situation.
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A Nash equilibrium is a situation where given what your opponents are doing, you are acting optimally (and that's true for everyone). It doesn't matter how your opponents would respond to you deviating, they simply assume that you are doing whatever it is that you're doing. So in the example if any of the guys recognizes that the others are going after brunettes he should go after the blonde (I personally prefer the darker haired ladies but the guys in the movie like the blondes). It's possible, as you suggest, that the scenario where one individual guy is going after the blonde and the rest are after the brunettes is not a NE but that also doesn't affect the conclusion that all going after the brunettes is not a NE.
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