Are you often fooled, if so! Then you must understand "game theory"

One. The origin of game theory

If you let mathematicians from all over the world vote: Who is the greatest mathematician from the last century to the present? The vast majority would not hesitate to vote for von Neumann. He is not only an outstanding mathematician, but also the founder of "computer science" and "mathematical economics". The learned genius died before the age of 54, a young man, in response to a sentence: genius is a candle lit from two ends, bright, but not long.

John von Neumann was born on December 3, 1903, to a traditionally conservative Jewish family in Budapest, Hungary. His father was a very successful banker, and in order to squeeze into the upper class, he paid for a knighthood, so their surname "Neumann" was preceded by the word "von", which was an honorific title for the nobility.

Von Neumann, the eldest of three sons, showed his distinctive brain, his unparalleled memory, at an early age. When he was a child, he only had to look at it slowly, and he could memorize the names and phone numbers on the whole page of the phone book, like a camera. Von Neumann regarded this as a game, and until he became an adult, he continued to "perform" his skills to his friends. Such an extraordinary memory made him extremely interested, in addition to science, he also liked history and philosophy, as long as he read, he remembered clearly. Von Neumann is famous for his profound knowledge, like an encyclopedia.

Before the age of 30, von Neumann showed extraordinary talent and achievements, publishing weighty research papers on "set theory", "algebra" and "quantum theory", becoming the youngest famous mathematician at that time.

In 1930, von Neumann came to the United States and became a visiting lecturer at Princeton University. That year he married Andreath.

Mr. and Mrs. Von Neumann are hospitable and the home is packed on weekends. His family has "parties" almost every week, entertaining colleagues and friends. Von Neumann was always the center of the salon, he had a good memory, a lot of jokes, he used jokes to enliven the atmosphere, and he liked to wear a clown's funny hat through the crowd and invite guests to relax and talk. From time to time, he still "toyed" with his superhuman memory, performing his shorthand phone book in public.

Von Neumann was inspired by the game of poker, generated deep thinking, and became the founder of "game theory". He doesn't play poker very often, he's not very lucky when he plays cards, and he's often a loser. The genius mathematician suddenly realized that the poker game was not only a problem of mathematical "probability theory", he lost the card because he always used "probability theory" alone to direct his own cards. In fact, the way to win lies in the use of strategy: on the one hand, to confuse the other party, on the other hand, to hide their intention information, you need to bluff. von Neumann began to study the "strategy of winning", and an important branch of mathematics " game theory " was born.

Von Neumann's genius also lies in the wide applicability of his pioneering research work, coupled with his own profound knowledge and ability to collaborate with people across disciplines. At the same time as he established a complete "game theory" theory, he realized that his mathematical research work would have an impact on "economics" and could apply "game theory" to guide economic strategy. He enlisted Morganstein, an Austrian economist working at Princeton at the time, to study the application of "game theory" in the field of economics. Later, the two co-authored a book, "Game Theory and Economic Behavior, Revolution in the Field of Economics", which became a classic work of "game theory" and the cornerstone of "mathematical economics". Although this book is only about "economics", its influence has spread to the disciplines of "psychology", "sociology", "political science", and "war military science", and has established the extremely important position of "game theory" in these fields.

Two. Why study game theory?

As early as the 20th century, it was predicted that game theory would be fully integrated into economics. Today, game theory has also become an important tool for us to discuss problems, from the bargaining of buying vegetables to the equilibrium problem under monopoly and competition conditions, all of which are permeated with the science of game theory, and the ideas and methods of game theory will surely become the mainstream and trend of the times.

The 1994 Nobel Prize in Economics was awarded to game theorists Hesani, Nash and Zeltai, which led to a profound revolution in game theory, which is not only used in economics, but also in other fields of social science, such as political science, law, sociology and even the military, game theory is becoming a useful analytical tool.

Military science takes war as the object of study, and war is complex and changeable, and it is an extremely complex large-scale social phenomenon. Game theory, on the other hand, uses its own characteristics to strive for the best outcome based on the worst-case scenario. In military struggles, where both sides usually do not have operational intelligence on the other, game theory is the best weapon in this uncertain situation. How to adopt tactics, select targets, set intelligence and disguise, and configure, especially deterrence theory, all play an important role.

All in all, game theory is a research tool for human behavior and is the sure way to win. So what reason do you have not to learn it?

Three. Basic concepts of game theory

Basic concept: Game refers to the process of selecting their own strategies based on the information they have to maximize their interests under the constraints of certain game rules, based on the environmental conditions of direct interaction.

This seems very confusing, in fact, for game theory you only need to remember the following 4 points:

1. The game can be competition or cooperation.

2. The game must learn to think in empathy.

3. The game only needs to be one step ahead and superior.

4. The game is that you have me, I have you, due to direct interaction, the benefits of game participants depend not only on their own strategies, but also on the strategies of other participants. The core of the game lies in rational empathy on the basis of overall thinking, using the benefits of others to speculate on the strategies of others, so as to choose the strategy that is most beneficial to themselves.

Four. A mini-game of game theory

Suppose there are 100 people in the class, and the professor needs each person to write down an integer between 1-100 on paper, and whoever writes the number is close to 1/2 of the average, and who wins the game.

You can try it for yourself which number you feel will win.

So let's analyze the game, first consider the most extreme case, assuming that everyone chooses 100, then the average is 100, and the average is half 50. So numbers greater than 50 are disadvantage strategies, so first of all, we must exclude it.

Then I think that the students in the class are rational thinkers, they will choose numbers below 50, so the average number is half 25, so I should choose a number of about 25, right.

But if my classmates are thinking about it one more level, the average is half 12.

……

By analogy, the answer to this question is infinitely closer to 1.

So you can see that in fact, the standard answer to this question for different groups of people is not the same, and the final result depends on the strategy of your opponent. The smarter the group number, the smaller it will be. Based on past experience, when the numerical result is less than 12: at this time it can be indicated that the group is excellent.

When the result is 12-16: the result shows that it is better.

When the result is 16-20: the result is good.

When the result is 20-25: the result is general.

When the result is above 25: the result is very poor.

So this example proves that your best strategy depends on the fact that you can take a step forward in the opponent's strategy, which will allow you to win the game.