What is the Prisoner's Dilemma?

Prisoner's dilemma refers to a special game between two arrested prisoners, explaining why it is difficult to maintain cooperation even when cooperation is beneficial to both parties. The prisoner's dilemma is a representative example of non-zero-sum games in game theory, reflecting that individual best choices are not group best choices. Although the predicament itself is only a model, similar situations often occur in real-life price competition, environmental protection, and interpersonal relationships.

Prisoner's Dilemma is

The story of the prisoner's dilemma is that two suspects were arrested by the police after committing the crime and were held in different rooms for trial. The police knew the two were guilty but lacked sufficient evidence. The police told everyone: if they both repudiated, each sentence was one year; if they both confessed, they were sentenced to eight years each; if one of them confessed and the other pleaded guilty, let out, and the custodial sentence was ten years. As a result, every prisoner faces two choices: frankness or repudiation. However, no matter what the associate chooses, the best choice for each prisoner is to confess: if the associate confesses, let it go if you confess, and if you do, you will be sentenced for one year. Compared with the ten-year sentence of denial, frankness is better than denial. As a result, both suspects chose to be frank and each sentenced to eight years in prison. If both people refused and each sentence was given for one year, this result is obviously good. The profound problem reflected in the prisoner's dilemma is that human individual rationality can sometimes lead to collective irrationality-smart human beings can become self-confidence or harm the collective interests because of their own intelligence.

Sorting out the basic game structure of the prisoner's dilemma can analyze the prisoner's dilemma more clearly.

The above examples may seem unnatural, but in reality, both human society and nature can find examples similar to the prisoner's dilemma, and divide the results into the same payment matrix. Economics, political science, and sociology in social sciences, as well as the disciplines of animal action and evolutionary biology in natural sciences can all use prisoner's dilemma analysis to simulate the game of biology facing endless prisoner's dilemma. The prisoner's dilemma can be widely used, illustrating the importance of this game. The following are examples from various circles:

Robert Axelrod in his book "

Psychological Game of Prisoners' Dilemma

When game participants can learn to estimate the likelihood of other players' betrayal, their own behavior is influenced by their experience of other people. Simple statistics show that, in general, the interaction of inexperienced participants with other participants is either typically good or bad. If they act on the basis of these experiences, (through more betrayal or cooperation, otherwise) they may be damaged in future transactions. As their experience grew, they gained a more realistic impression of the possibility of betrayal and became more successful in participating in the game. Fail

Prisoner's dilemma

The impact of early transactions experienced by experienced participants on their future participation may be much greater than the impact of these transactions on mature participants. This principle explains in part why young people's growth experience is so influential, and why they are particularly vulnerable to bullying, and sometimes they themselves end up being bullies.

The possibility of betrayal in the group can be weakened by the experience of cooperation, because the previous game established trust. So self-sacrifice can, for example, strengthen the moral character of the group. If the group is small, positive behavior is more likely to get feedback in a mutually positive manner--encouraging individuals in the group to continue working together. This is related to a similar dilemma: Encourage those you will aid to be satisfied with actions that could put them at risk. Such methods are mainly involved in the study of reciprocal altruism, group selection, blood selection and moral philosophy.

Prisoner's dilemma closes deals

Hofstadter once suggested that problems such as the prisoner's dilemma would be easier to understand if they were explained in the form of a simple game. For example, he used a simple game of "closed bag transactions" to illustrate this topic:

The two exchange face-to-face closed bags with each other to understand that one side puts money and the other puts the goods. The two parties can honestly put things in the bag and exchange them according to the promise; or they can give the other party empty bags and choose to betray.

In this game, because betrayal can obtain huge benefits, many people must choose to betray. This means that rational merchants will not conduct such transactions, and the "closed bag transaction" will lose the market due to adverse selection. ^[3]

Prisoner's dilemma is enemy or friend

"Is the enemy or the friend?" Is a competition show, which was screened on the GameShow Network from 2002 to 2005. This is an example of a prisoner's dilemma game with real people, but the scenario is artificial. The competition involved three pairs of people. When each pair is eliminated, they play a prisoner's dilemma game to decide how to divide their prizes. If they all collaborate ("friends"), their prizes are divided equally. If one cooperates and the other betrays (the "enemy"), the betrayer gets all the prizes, and the collaborators get nothing. If they both betrayed, then both would find nothing. Note that this payment matrix is different from the aforementioned standard payment matrix, because the loss is the same in the case of "all betrayal" and "the betrayal of my cooperation. Compared with the stable equilibrium of the standard prisoner's dilemma, "all betrayal" is an unstable equilibrium (weakequilibrium). If you know that your opponent will be an "enemy", then your choice cannot influence your prize. In a sense, "is the enemy or the friend" has a payment model between "Prisoner's Dilemma" and "Chick".

This payment matrix is:

If the participants cooperate, each gets +1.

If you betray each, you get 0.

If A cooperates and B betrays, A gets 0 and B gets +2.

Friends or foes will be useful to anyone who wants a realistic analysis of the prisoner's dilemma. Note that participants can only play once, so all ideas involving repeated games are not applicable, and the "tooth for tooth" strategy cannot be developed. ^[4]

In the case of friend or foe, each contestant is allowed to make a statement to convince the other half of his friend to be friendly before the two parties secretly decide to cooperate or betray each other. Probably the way to "break the system" would be for a participant to tell his opponent: "I would choose to be an enemy. If you believe I will share the prize with you later, choose to be a friend. Otherwise, if you choose to be an enemy, we Will return empty-handed. "A more greedy version would be:" I will choose to be the enemy. I will give you X percent, and the remaining (100-X) percent belongs to me. So, yes or no, Either we all get some, or we all get nothing. "(In the ultimatum game.) Today, the trick is to minimize that X percent and keep another competitor still choosing to be a friend. Basically, the participant must know the limit, where the utility of his opponent from seeing him gain nothing more than the utility of the money he is sure to win, if he goes well.

This method has never been tested in competitions; it may be because referees will not allow it, and even if it does, inequality aversion will result in lower expected returns due to the use of this rule. (This method was tried in the ultimatum game, which resulted in rejection of high and unequal bids-in some cases, the equivalent of two weeks' wages took precedence over the two participants being denied nothing.)