Purification theorem | Wikipedia audio article
Channel: wikipedia tts
Date: 27/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Purification_theorem


00:01:46 Example
00:05:01 Technical details



Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.

Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain

Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.

Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services/invoke/uid/0000001a130b3f91
Other Wikipedia audio articles at:
https://www.youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.8018873822432234
Voice name: en-US-Wavenet-B


"I cannot teach anybody anything, I can only make them think."
- Socrates


SUMMARY
=======
In game theory, the purification theorem was contributed by Nobel laureate John Harsanyi in 1973. The theorem aims to justify a puzzling aspect of mixed strategy Nash equilibria: that each player is wholly indifferent amongst each of the actions he puts non-zero weight on, yet he mixes them so as to make every other player also indifferent.
The mixed strategy equilibria are explained as being the limit of pure strategy equilibria for a disturbed game of incomplete information in which the payoffs of each player are known to themselves but not their opponents. The idea is that the predicted mixed strategy of the original game emerge as ever improving approximations of a game that is not observed by the theorist who designed the original, idealized game.
The apparently mixed nature of the strategy is actually just the result of each player playing a pure strategy with threshold values that depend on the ex-ante distribution over the continuum of payoffs that a player can have.  As that continuum shrinks to zero, the players strategies converge to the predicted Nash equilibria of the original, unperturbed, complete information game.
The result is also an important aspect of modern day inquiries in evolutionary game theory where the perturbed values are interpreted as distributions over types of players randomly paired in a population to play games.