A guess game

One day in 1987, a strange quiz advertisement appeared in the Financial Times, inviting bankers and businessmen to participate in a digital quiz competition. Participants must choose an integer between 0 and 100 to send back. Whoever guesses the number is closest to two-thirds of the average of the sum of all numbers, who is the winner. If there are more than one person guessing the number, then the only winner will be selected by random draw. The prize is a round-trip ticket from Concord’s first class from London to New York, worth more than \$10,000.

Imagine if you also participated in the quiz, how would you choose the numbers? According to traditional economics, you will rationally choose a number, but how to choose is rational?

You obviously don’t know which number others will choose, so it’s a bit difficult to be rational. So, you might have a rough guess at first: maybe the number chosen by people varies randomly from 0 to 100, so the average is about 50, so 33 would be a good choice because 33 is close to 50. Two-thirds. You sent this number with expectation and then came up with an obvious question – what if the rest of the people are as you think?

If that’s the case, then other people will choose a number of around 33, so the average is not 50, but 33 or so, then two-thirds of 33 is 22. You can send this number back, or follow this line of thought and think again. If the others are the same as you think, then the average is 22, so the best guess is actually around 15.

By the way, the more you think about it, the smaller the number will become, and the real question will come. Which number should you stop on? Continuing with this logical reasoning, you will begin to suspect that everyone will choose a very small number, or even zero. In fact, the number 0 is also an answer to the mathematical logic, because two-thirds of 0 is still 0, and everyone chooses 0, then everyone guesses right. Rational economists will choose 0, but will everyone else choose this besides them?

As a result, there are indeed others who have chosen 0, but not many. This strange guessing game was designed by Richard Taylor of the University of Chicago. When he listed the numbers sent, he found that a few people really chose 0, and many of them chose Yes 33 and 22 – Logical thinking stops at the first or second step. The final statistical result, the average is 18.9, and the winner chose 13.

Taylor’s design of this guessing game is mainly to show that the behavior of people in the minds of rational economists is obviously inconsistent with real life. The idea that people should choose the number 0 comes from the traditional theory of economics, which is the “gametheory” that everyone knows. It discusses how rational people can have the best in a competitive environment. Behavioral performance.

In the 1950s, the mathematician John Nash – the prototype of the recent story of the film ABeautifulMind – proved that a rational person knows that his competitors are also rational. Many times he always finds a “best” strategy to use. So, in Taylor’s guess game, the best strategy is to choose 0. Because if everyone is completely rational, then they will choose the same number, and 0 is the only number equal to two-thirds of the average.

But the problem is that if a rational economist comes to participate in this quiz, he will definitely lose. In fact, guessing is neither irrational nor clever, but it is only innocent, especially when they think about human behavior too simple. An economist can try to make himself rational, but he can’t control others as rational as him.

This quiz game is not a purely mathematical problem, because the best number is based on the actual number chosen by everyone, and no one knows how crazy people will choose those numbers. As a result, this quiz game has nothing to do with the game theory of the rational family, but it is very important that we encounter real-life situations similar to this game every day, and relying solely on reasoning and logic can’t cope.

For example, driving to work in the morning, in order to avoid traffic jams, you will want to choose a path that others will not go. However, other people will think so. As a result, your thoughts become, many people are trying to do something that most people won’t do, but rationally, this is impossible because people can’t guess the minds of others. Think about stock trading again, because it involves a lot of money, so you should always be profitable if you want to take action rationally.

actually not. There is an old argument in economics that the price of a stock must reflect its fair and reasonable value, because investors are rational, they will buy stocks with undervalued value, so that stock prices will rise, or they will sell those high value. Estimated stock until the stock price falls. Rational investors do this because they can easily earn money in the process.

However, things are not that simple. Suppose some smart people find that the price of individual stocks is very low. In order to make a profit easily, they may rationally buy positions, thinking that when the stock price rises to its worth, they will sell and make a profit. But, like the rational economists in Taylor’s guessing game, their views on stocks may be right, but they make people think too simple. Because there are still irrational investors, they have no information at all, and there is no good reason to hold this stock. If they feel that they will lose money, they will continue to sell, making the stock price fall even lower. No matter how ridiculous and annoying it seems, they will still do it.

Therefore, an absolutely rational investor in the stock market will also lose money. Because the operation of the stock market is based on people’s beliefs, and different people have different beliefs and ideas, it is too strange to strive to be rational in this case.

If you think that the temperature in Cleveland can affect the stock market enough, then the temperature of the city can really affect the stock market, so as a wise investor, it is best to check the weather conditions in Cleveland before buying and selling stocks, even if This sounds “irrational”. To put it bluntly, reason is just a tool that can be used at some point. Even this tool can only stay at the theoretical level.

There may be others who hope to preserve the theory of rational choice, but for them, continuing to explore will only make the situation worse. Even sometimes, before making a logical decision, most of us will not do the calculations that children will do. So it seems that mistakes are the genes that we humans can’t afford.