This TED-Ed lesson has featured a great deal of discussion about concepts that are already assumed you were somewhat familiar with in game theory, namely Nash equilibrium and rationality. For more discussion about these topics, the following TED-Ed videos may be up your alley.

This video explains the psychology of rationality and discusses the limits of this kind of thinking more generally.

This lesson discusses Nash equilibrium from another angle, explaining why businesses cluster together even though you might think they shouldn’t.

This final video tests your knowledge of Nash equilibrium with a fun ultimatum game.

In game theory, the 2/3 the average game, though simple, is incredibly influential because it showed the failings of solution concepts like Nash equilibrium in the real world. While the formalization of k-level games is relatively new, the idea has been around for at least 80 years, and can be traced at least to the famous economist John Maynard Keynes.

When thinking about how stock traders trade on the stock market, he likened the best strategy to the strategy one would employ if they were trying to pick the prettiest (or most handsome) person, in a hypothetical “beauty” contest, saying:

"It is not a case of choosing those [faces] that, to the best of one's judgment, are really the prettiest, nor even those that average opinion genuinely thinks the prettiest. We have reached the third degree where we devote our intelligences to anticipating what average opinion expects the average opinion to be. And there are some, I believe, who practice the fourth, fifth and higher degrees." (Keynes, General Theory of Employment, Interest and Money, 1936).

In an experiment by the radio show Planet Money, they tested this idea with 12,000 participants and photos of 3 cute animals. They asked a random half which they thought was the cutest, and other half which everyone else would think was the cutest. Sure enough, the answers were very different. You can listen to that informative podcast here.

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