Johnf nash, winner of the Nobel Prize in Economics from 65438 to 0994, Princeton University, USA. Nash won the Nobel Prize in Economics for his contribution in the field of game theory. He put forward the Nash equilibrium theory, and the most well-known story about game theory is called "Prisoner's Dilemma":
It is said that one day, a rich man was killed at home and his property was stolen; In the process of detecting the case, the police arrested two suspects, Zhang San and Li Si, and found the lost property in the victim's house from their residence. However, they denied killing anyone and argued that they only stole something. So the police isolated the two and put them in different rooms for trial. The police said to Zhang San and Li Si respectively, "Because you have conclusive evidence of theft, you can be sentenced to 1 year in prison. But I can make a deal with you. If you confess to murder alone, I will only sentence you to three months' imprisonment, but your partner will be sentenced to 10 years' imprisonment. If you refuse to confess and are reported by your partner, you will be sentenced to 10 years in prison, and he will only be sentenced to 3 months in prison. However, if you all confess, then you will all be sentenced to five years in prison. "
How about Zhang Sanhe and Li Si? They are faced with a dilemma-confession or denial. Obviously, the best strategy is that both sides deny it, and as a result, everyone only gets one year. But because they are isolated, they cannot collude with each other. According to Adam Smith's theory, everyone is a "rational economic man" and will make choices for the purpose of self-interest. These two people will have such a calculation process: if he confesses, I will go to prison for 10 years if I don't confess, and he confessed for only 5 years, so it's a good deal; I confess, he confesses, and he goes to jail for five years. If he doesn't confess, I will only sit for three months, and he will sit in prison for 10 years, which is also very cost-effective. Considering the above situation, whether he confessed or not, it was a good deal for me. Both of them can use this kind of brain. In the end, both of them chose the trick? As a result, they were sentenced to five years in prison. The strategy (denial) and the ending (sentence 1 year imprisonment) that were originally beneficial to both sides will not appear. This is the famous "prisoner's dilemma". It actually reflects a very profound problem, that is, the contradiction between individual rationality and collective rationality.
In fact, if both of them are negative, each sentence is 1 year, which is obviously better than five years in both sentences, but it can't be done in practice because it doesn't meet the requirements of individual rationality. As a rational person, Zhang San and Li Si will think that if I deny it and the other party confesses, I may be sentenced to 10 years, and rational people will not take such risks. But as a result of rational choice, Zhang San and Li Si were both sentenced to five years, and the best result of being sentenced to 1 year did not appear. In other words, it is a rational choice for everyone, but it is irrational for the whole group.
This is contrary to the conclusion of traditional economics. Traditional economics holds that there is an "invisible hand" in the market economy, and the result of its adjustment is that everyone's rational choice will eventually lead to the maximization of the interests of the whole collective. In fact, just like the prisoner's dilemma, this invisible hand will lose its function when only a few people participate in the choice, because at this time, people's decision-making process will consider the ideas of other participants, just like gambling and chess, which is exactly the same as the perfect competition when there are a large number of buyers and sellers, and needs a new set of ideas to study.
In the above example, we noticed a non-optimal result, that is, both of them chose Frank strategy and were sentenced to five years. This result is called "Nash equilibrium", also called non-cooperative equilibrium. The most basic concept in game theory is Nash equilibrium. When it comes to game theory, the most talked about and the most famous is "Nash equilibrium". Nash equilibrium refers to such a strategy combination, which consists of the optimal strategies of all participants. That is to say, given other people's strategies, no single participant has the initiative to choose other strategies to make himself gain greater benefits, so no one has the initiative to break this equilibrium.
Of course, although "Nash equilibrium" is composed of a single person's optimal strategy, it does not mean that it is an overall optimal result. As mentioned above, in the case of conflict between individual rationality and collective rationality, the final outcome of everyone's pursuit of their own interests is a "Nash equilibrium", which is also an unfavorable outcome for everyone.
In this sense, the paradox put forward by Nash equilibrium actually shakes the cornerstone of western economics. At the same time, it also reminds us that cooperation is a favorable "self-interest strategy". In fact, if the above-mentioned two prisoners can collude, then they will definitely choose to deny both and be sentenced to 1 year for theft. Of course, it is with this in mind that the police conducted an isolation review on them to find out the truth, and the most beneficial cooperation result for the prisoners did not appear. Nash equilibrium describes the non-cooperative game equilibrium. In reality, non-cooperation is more common than cooperation. Therefore, "Nash equilibrium" is a significant development of the cooperative game theory of von Neumann and Morgan Stern, and even a revolution.
Nowadays, Nash equilibrium is widely used in various research fields, especially in institutional analysis. Applying it, we can draw a very important conclusion: an institutional arrangement must be a Nash equilibrium if it is to be effective. Otherwise, this institutional arrangement cannot be established.