What Is a 'Nash Equilibrium'?

<A Beautiful Mind> is a film about the life of the American genius mathematician John Nash.
Nash won the Nobel Prize in Economics in 1994 for the 'Nash Equilibrium' he presented in his doctoral dissertation.
The film includes a scene in which Nash comes up with the idea of the 'Nash Equilibrium'.
Until then, economics had widely accepted the argument of Adam Smith that rational individuals, that is, each economic agent acting 'selfishly' in their own interest, also bring benefits to society.
Nash, however, says that Adam Smith's theory is incomplete.
This is because he discovered situations in which people make the best choices for their own interests, yet these do not lead to the socially optimal outcome.
A situation in which each individual makes the best, most rational choice, yet everyone ends up worse off: Nash won the Nobel Prize in Economics in recognition of his analysis of this paradoxical situation.
Nash equilibrium theory refers to a state of equilibrium in which, when each party makes the best choice in response to its competitors, no one changes their choice; it is a state in which, on the premise that the other party maintains its current strategy, I also have no incentive to change my current strategy.
This is closely related to the Prisoner's Dilemma: if China and the United States cooperate with each other, both gain, but if one of the two countries betrays the other, only the betraying country gains, and if neither cooperates, the result is negative for both.
Aumann's folk theorem holds that countries that are initially uncooperative because they look out only for their own interests can reach a cooperative equilibrium in which everyone prospers together if the same situation is repeated.