Game Theory 101 (#70): The Purification Theorem

The purification theorem says that almost all mixed strategy Nash equilibria can be reconceptualized as close approximations of pure strategy Bayesian Nash equilibria, in which the relative probabilities of taking each action are nearly identical. Thus, if you don't believe that players don't mix in real life, this isn't a problem: mixed strategy Nash equilibria are essentially pure strategy equilibria in disguise.

Bonus note: John Harsanyi came up with the purification theorem. This was a major reason why he won a Nobel Prize in the same year of John Nash's victory.

[dominiclebron]

i love the real-world POV explanation about liking games, and how randomizing is definitely necessary in certain situations.
But u really connect w/ your audience when u use self-examples as such.

[PunmasterSTP]

I heard that when playing games with cats, you can make use of the…purrr-ification theorem 😎

But seriously, these videos are amazing. Thank you so much for all of them!

[wenshan]

thanks for the great lecture ! i have something to clarify
at 14:30 - the last equation for p, is there a typo?
because (10 + 2 - E^2) does not converge to 10 when E -> 0
Shouldnt it be (10 + E - E^2) instead?

[chrisistasty]

Typo at 9:18? The bottom red Theta should have subscript 2 not 1? Love yr vids btw

[elnoch]

Thanks for the lecture. One question, does it matter how do you perturb the game? I mean, you left the bottom right payoff unchanged, is there a reason for it?

[zhengyuancui]

I get your idea but think that this is a stupid idea. Understanding something easy from something difficult and not that connected.

[YearwigY]

Hey mate is the Purification Theorem in your book?