A game will eventually form a result, just like bargaining, which is game equilibrium. Nash equilibrium is the most common and important game equilibrium. It was put forward by American genius mathematician Nash when he was studying for his doctorate at 1950. The topic of this paper is "Equilibrium Problem of Multi-player Game". Nash skillfully used mathematical skills to prove the following theorem: for any non-cooperative game with n players (zero-sum or non-zero-sum game), if each player's strategy is limited, then there is at least one Nash equilibrium solution set. The paper is only a short page, but it has become a classic document of game theory and won him the Nobel Prize in Economics.

The classic case of Nash equilibrium is "prisoner's dilemma": two suspects are locked in two cells, and the police tell them that if they both confess, they will be imprisoned for three years each; If both of them don't confess, let them go; If one confesses and the other doesn't, the confessor will be imprisoned for 3 years, and the one who doesn't will be imprisoned for 10 years. In the eyes of outsiders, it is best for both of them not to confess. But from everyone's point of view, the cost of recruiting and not recruiting is {3; 3} and {0; 10}, it is better to confess.

However, a paradox is drawn from Nash equilibrium: the optimal choice of a single person will not lead to the global optimal result. There are many examples in reality, for example, the result of price war is that both sides lose. "Nash equilibrium" proves a truth: the dilemma cannot be solved under the condition of non-cooperative game.