On "Game Theory"

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I haven't found it before, but after learning the basic knowledge of game theory, it's easy to find that games are around us like air and everywhere. How to play the big

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I haven't found it before, but after learning the basic knowledge of game theory, it's easy to find that games are around us like air and everywhere. How to play the big and small things in life, the following content will be explained.

? Whether in daily life or at work, "game" is a high-frequency vocabulary. What is the relationship between the game in life and the game in economics? Will people who are proficient in "games" be particularly good at "routines" and what kind of thinking is "game theory"? Let's talk about it from the following aspects.

First, the definition of game theory

? Game theory means that in an equal game, two people use each other's strategies to change their confrontation strategies in order to win. The idea of game theory has existed since ancient times. China's ancient works, such as The Art of War, are not only military works, but also the earliest game theory works.

Second, the development of game theory.

At first, game theory mainly studied the winning or losing of chess, bridge and gambling. People's grasp of the game situation only stays in experience and has not developed into theory. Modern research on game theory began with Zemelo, borell and von Neumann.

? 1928, von Neumann proved the basic principles of game theory, thus announcing the formal birth of game theory. 1944, the epoch-making masterpiece Game Theory and Economic Behavior written by von Neumann and Morgenstein extended the two-player game structure to the n-player game structure, and systematically applied the game theory to the economic field, thus laying the foundation and theoretical system of this discipline.

In 1950 ~ 195 1, John Forbes Nash proved the existence of equilibrium by using the fixed point theorem, which laid a solid foundation for the popularization of game theory. Nash's groundbreaking papers such as Equilibrium Point of N-person Game (1950) and Non-cooperative Game (195 1) give the concept of Nash equilibrium and the existence theorem of equilibrium. In addition, the research of Reinhard Zelten and John Hasani also promoted the development of game theory. Today, game theory has developed into a relatively perfect discipline.

Third, examples of game theory.

There are some classic and thought-provoking cases in Game Theory, which not only fascinates professional researchers, but also interests some ordinary people. It has not only become a beautiful landscape in "game theory", but also an academic spectacle in the whole field of economics.

Prisoner's dilemma

The story of "Prisoner's Dilemma" tells that two suspects were caught by the police after committing a crime and were held in different rooms for interrogation. The police knew that the two men were guilty, but they lacked sufficient evidence. The police told everyone: if both people deny it, they will be sentenced to one year each; If both confess, they will be sentenced to eight years each; If two people have a confession, a denial, a confession, and a denial, they will be sentenced to ten years. Therefore, every prisoner is faced with two choices: confession or denial. However, no matter how the partner chooses, the best choice for every prisoner is to confess: if the partner denies it, he will be released, and if he denies it, he will be sentenced to one year. Confession is better than no confession; If your partner confesses and confesses himself, you will be sentenced to eight years. Confession is better than denial. As a result, both suspects chose to confess and were sentenced to eight years in prison. If both of them deny it, it is obviously a good result to sentence them to one year each. But this Pareto improvement can't be done, because it can't meet the rational requirements of human individuals.

The profound problem reflected by the prisoner's dilemma is that the individual rationality of human beings sometimes leads to the collective irrationality-smart human beings will be trapped by their own cleverness or harm the collective interests.

? A few years ago, in China color TV market, manufacturers chose to cut prices sharply based on their own interests, but the price war caused by this made all manufacturers suffer heavy losses, which was also a prisoner's dilemma.

Erzhizhu game

There are two pigs in the pigsty, one is big and the other is small. The pigsty is very long, with a pedal at one end and a discharge port and a trough at the other. Every time you step on the pedal, a small amount of food will fall on the feeding port on the other side of the pigsty far from the pedal. If one pig steps on the pedal, the other pig has a chance to eat the food that has fallen on the other side first. As soon as the pig steps on the pedal, the big pig will eat all the food just before the pig runs to the trough; If the big pig steps on the pedal, there is still a chance for the little pig to run to the trough and compete for the other half before eating the fallen food. Therefore, in order to be full, the best strategy for pigs is the "hitchhiking" of big pigs. This situation can be seen everywhere in reality.

For example, a new product has just been listed, and its performance and function are unfamiliar. It is not only small enterprises that produce new products, but also other enterprises with stronger production and sales capabilities. Then, there is absolutely no need for small enterprises to be the first bird and invest a lot of advertisements to promote their products, as long as they adopt the follow-up strategy.

The "smart pig game" tells us that whoever steps on this pedal first will benefit, but not necessarily much effort.

Three Nash equilibria

? The core of Nash equilibrium is actually the idea of mutual benefit. There is a little story that can be reflected. There are two small shops near the street, one selling porridge and soybean milk and the other selling fried dough sticks and steamed bread. Generally, customers buy steamed bread, fried dough sticks, porridge and soybean milk, so at first, the business of the two stores was very prosperous. Later, the seller of soybean milk felt that there was a contradiction between the two sides when selling fried dough sticks to grab business. The seller of fried dough sticks left, and his business was not good as a result.

In fact, there are many examples related to games in our life. In such a complex game battlefield, how to get the maximum benefit in the game field is a university question. Therefore, game theory is a very useful subject. Through reading and studying, I know a little more about learning.