Prisoner's Dilemma: Trust is priceless, betrayal is priceless

Let’s look at a story:

The police captured two suspects A and B. They committed the crime together. The police put them in two rooms for isolation interrogation. Neither of them knew what their companion had said to the police.

The police policy is "lenity for those who confess, severity for those who resist":

1. If both people plead guilty, each will be sentenced to 5 years;

2. If neither person pleads guilty, each will be sentenced to 1 year;

3. If only one person pleads guilty, the person who pleads guilty will be released, and the person who does not plead guilty will be sentenced to 10 years.

If you were one of the prisoners, what would you choose?

Of course, from the perspective of bystanders, it is clear that the optimal strategy is for both of them to choose not to plead guilty, that is, to cover up the other party, and each person will only be sentenced to one year.

However, as the prisoner involved, the heart is very complicated. See the analysis below:

Taking prisoner A as an example, there are two possibilities for prisoner B to plead guilty or not to plead guilty.

1. Prisoner B did not plead guilty. There are two situations:

(1) Prisoner A pleads guilty and will be released without charge;

(2) Prisoner A does not plead guilty and will be sentenced to 1 year.

(1)(2) In comparison, for prisoner A, confessing is a better strategy.

2. Prisoner B confessed. There are two situations:

(1) Prisoner A also pleads guilty and will be sentenced to 5 years;

(2) Prisoner A does not plead guilty and will be sentenced to 10 years.

(1) (2) In comparison, pleading guilty is still the optimal solution for Prisoner A.

From the analysis of the above two situations, it is not difficult to find that no matter prisoner B chooses to plead guilty or not, prisoner A's optimal strategy is to plead guilty.

In this way, as long as the two prisoners are rational enough, they will almost certainly choose to confess and receive leniency. Each will be sentenced to 5 years, and no one will take advantage.

This is the prisoner's dilemma first proposed by Princeton University mathematician Albert Tucker in 1950. The analysis is shown in the figure below:

The prisoner's dilemma is A unique game theory between two arrested prisoners. It is a representative example of a non-zero-sum game in game theory.

When personal interests conflict with collective interests, people tend to pursue personal interests first. When everyone only considers self-interest, the result is often harming others and not benefiting oneself.

The Prisoner's Dilemma illustrates why it is difficult to maintain cooperation even when cooperation benefits both parties. Reflecting an individual's best choice does not reflect the group's best choice.

Although the dilemma itself is only of a model nature, there are many examples of the prisoner's dilemma in reality. For example, in reality, similar situations will occur in price competition, environmental protection, interpersonal relationships, etc.

For example, in the price reduction of color TVs a few years ago, manufacturers made choices like prisoners in order to maximize their own interests:

If the price is reduced, they can win a larger market . If prices are not lowered and others lower prices, others will occupy a larger market.

Therefore, no matter what others do, for our own factory, price reduction is the best choice. When every manufacturer made such a choice, the color TV market started one round of price war after another. The result was heavy losses in the end.

Lu said, understand the prisoner's dilemma in one sentence: Betrayal also has a price, and smart people know how to make the price large enough to prevent the other party from betraying.

How to get rid of the prisoner's dilemma, see the analysis below:

1. Increase the cost of betrayal.

Make it clear in some way what the punishment will be if betrayal occurs.

If two prisoners know where the other's home is and can threaten the safety of the other's wife, children, and children, then the possibility of betrayal between them will be reduced.

In many historical stories, in order to form an alliance, the two parties would use their sons as hostages as collateral, or marry their daughters off, such as the marriage between Princess Wencheng and Songtsen Gampo.

Granting certain shares to employees and agreeing on liquidated damages in contracts are essentially intended to increase the other party’s betrayal costs! Betrayal also has a price!

2. Introducing a third party.

It is also a very common business strategy to introduce an external monitoring station to reduce the chance of betrayal by both parties in the game.

For example, third-party payment, Alipay, endorsement, guarantee, notarization, pre-marital property justice, etc., use the third party as a credit intermediary to eliminate or reduce the possibility of betrayal between buyers and sellers!

3. Repeated games.

If the same game is repeated, for example, if these two prisoners are caught 100 times in a row, will they dare to betray each other easily?

In such a game, any betrayal will lead to the other party's next revenge. If I betray you this time, you will double betray me next time!

This makes me betray you, which will do more harm than good.

It is precisely because of this that everyone tends to cooperate with each other!

You went to a tourist attraction and it started to rain heavily. At this time, an umbrella that usually costs ten yuan in a store near your home sells for fifty yuan at the tourist attraction. Do you want to buy it?

You still have to buy it. For the tourist attraction merchants, even if they sell you ten yuan this time, your chance of going to their house to buy something again is almost zero. But the store near your home is different. He still points you to continue to patronize his store.

Invest in yourself and not be a prisoner. Even if you are a prisoner, we will have to reduce your sentence by a few years. Is this true?

Invest in yourself and make yourself more valuable to increase your weight and control. You will have more freedom when making choices and will not easily fall into the prisoner's dilemma.

Even if you become a prisoner, the benefits you bring to the other party are much higher than the benefits that the other party can create after betraying you, which will also increase the cost of the other party's betrayal.

Even if the other party betrays you, its advantages can quickly attract new partners, the losses will be much smaller, and you will be spared a few years in prison.

Personal interpretation, for reference only, to inspire discussion, welcome to leave a message for discussion.