The game theory is, after all, a branch of mathematics, more precisely, of preparatory science, and it is natural to talk about the mathematics language, and amateurs seem to be just a bunch of mathematical formulas. It is good that game theory is concerned with everyday economic life, so it cannot be free of human fireworks. In fact, this theory is a term borrowed from issues of a competitive, confrontational and decision-making nature, such as chess games, poker and war, which sounds somewhat illuminating, but is in fact of great relevance. The masters of game theory see economic and social problems as a chess game, often deeply rooted in the game. So, it is not boring to start with the small things of human beings in our daily lives, to use the stories around us as examples. One day, a rich man was killed in his home and his property was stolen. During the investigation of the case, the police caught two suspects, skarfis and nakuls, and found the missing belongings in the victim's home from their residence. They denied, however, that they had killed people, arguing that they had first discovered that the rich had been killed and then simply stole something. The police then isolated the two persons and held them in separate rooms for interrogation. The district prosecutor spoke to each individual separately. The public prosecutor said, “you can be sentenced to one year's imprisonment for theft because you have solid evidence. But i can make you a deal. If you confess to the murder alone, i will only sentence you to three months' imprisonment, but your accomplice will be sentenced to 10 years' imprisonment. If you refuse to confess and are reported by your accomplices, you will be sentenced to 10 years ' imprisonment and three months ' imprisonment. But if you both confess, then you will all be sentenced to five years' imprisonment.” what about skarvis and nakuls? They face a dilemma — confession or denial. It is clear that the best strategy is for both sides to deny, with the result that everyone will be sentenced to only one year. However, because of the isolation of the two persons, they were unable to supply a confession. So, according to adam smith's theory, everyone is acting for their own ends and they choose to confess as the best strategy. Because a confession can expect a very short period of imprisonment — three months — but it would obviously be better for the partner to deny it than for 10 years. This strategy is a strategy for personal gain. More than that, there is more to confess. If the other side confesses and denies it, it's 10 years. It's too bad! In this case, therefore, the choice should still be made to confess, even if they do so at the same time, with a maximum of five years, better than 10 years. Therefore, the reasonable choice between the two persons was to confess, and the strategy (denial) and outcome (one year's imprisonment) that would have favoured both sides would not have emerged. Both of them opted for a confessional strategy and the resulting five-year sentence was called the “nash balance” or non-cooperative balance. Because each party chooses a strategy without a “complicity” (coercive supply), they choose a strategy that is in their best interests, regardless of social welfare or the interests of any other counterparty. In other words, this mix of strategies consists of the best mix of strategies among all bureau members (also known as parties, participants). No one will take the initiative to change their strategies so that they can benefit more. “the prisoner's dilemma” has a broad and profound meaning. The conflict between individual and collective rationality and the ultimate result of each individual's pursuit of self-interest is a “nash balance” and an outcome that is not conducive to all. Both of them were the first to think of themselves in a strategy of confession and denial, so that they were bound to serve long sentences. The outcome of imprisonment for the shortest period of time can only be obtained when they are all first thinking of each other or conspiring with each other. The “nash balance” first challenged adam smith's principle of “unseen hands”. According to smith's theory, in a market economy, every person proceeds from his or her own ends, and ultimately society as a whole achieves its altruistic effects. Let us recall the famous words of this economic saint in the state richness: “in pursuing his own (personal) interests, he will often be more effective in promoting social interests than he actually wants to do.” a paradox that emerges from the "nash balance" principle of invisible hands: from the point of view of profit, the result is to harm the person, to his detriment and to his detriment. That is the fate of the two prisoners. In this sense, the paradox of the “nash balance” actually shakes the foundations of western economics. Thus, from the “nash balance” we can also discern the truth: cooperation is a favourable “self-serving strategy”. But it must conform to the golden law that you treat others as you wish, but only if they do so. In other words, the chinese say, “i do not want to do anything”. But only if man does not do to me what he wills. Secondly, the “nash balance” is a non-cooperative game, and in reality cooperation in central africa is more common than cooperation in general. So the “nash balance” is a major development, if not a revolution, of the theory of a collaborative game between von neumann and morgan stern。
