Nash Equilibrium

A development by American mathematician John Nash, for which he was awarded the Nobel Prize for Economics.

Adam Smith says that the common good will be served if each individual looks after their own self-interest.

: [Er: no he doesn't. That's a caricature, although a common one. -- JasonGrossman]

John Nash qualifies that. He says that a group, within which everybody looks after their own self interest without cooperation, can get stuck in a local maxima of the common good, arbitrarily far from the greatest possible common good.

A Hollywoodified version of Nash's life story is presented in the mediocre Oscar winner A BeautifulMind. The book of the same name is excellent, however.