What does the Prisoner Puzzle story illustrate? Let s give an example of how to effectively solve th

Are you referring to the prisoner's dilemma in the Nash equilibrium? Let me explain that two thieves, A and B, commit a joint crime and get caught by the police by entering a private house. The two men were placed in two separate rooms for interrogation, and the policy given for each suspect was:

If a suspect confesses to the crime and hands over the stolen goods, then the evidence is conclusive and both are found guilty. If the other suspect also confesses, both are sentenced to 8 years in prison; If the other suspect does not confess but denies it, the sentence for obstructing official duties (because there is evidence that he is guilty) is increased by two years, and the confessor is credited with a reduced sentence of eight years and released immediately. If both of them deny it, they cannot be convicted of stealing due to insufficient evidence, but they can be sentenced to 1 year in prison for the crime of trespassing into a private house.

The table gives the payout matrix for this game. Table Prisoner's Dilemma Game A B Confession Denial Confession -8,-80,-10 Denial -10,0-1,-1 After drawing the above game matrix, you can see that for the two, the best outcome is to deny both, and both of them will be 1 year each, which is the shortest time in prison overall. However, since A and B are isolated from each other, they cannot communicate with each other, and according to the hypothesis in economics, A and B are both self-interested as rational economic beings, so they will start to calculate, let's take A as an example:

A will consider that if B chooses to confess, then, if he also confesses, he will be sentenced to 8 years, and if he denies, he will be sentenced to 10 years, so if B chooses to confess, A will choose to confess; If B chooses to deny, then if he confesses, he can be acquitted, and if he denies, he will be sentenced to 1 year, so if B denies, then A still chooses to confess. Therefore, no matter how B chooses, A will choose to confess. In the same way, this is the way of thinking on the B side, and he will eventually choose to confess.

In the end, both men would be sentenced to eight years. The Nash equilibrium is a well-known theory in economics, the prisoner's dilemma is the basic Nash equilibrium, which is a one-round Nash equilibrium, that is, they only need to make one decision, and the extended Nash equilibrium is a multi-turn game. If LZ is interested, you can add me QQ or continue to ask, I am willing to answer for you.

There's a comprehensive introduction to microeconomics, but I don't remember it. Look for it yourself.

Case Study: The Prisoner Dilemma Match.

Let's say you're playing a prisoner's dilemma with a "suspect" who is locked up in another room. Moreover, imagine that this game is not played once, but many times. The final score you get for your game is the total number of years you have been imprisoned.

You want to make that score as low as possible. What strategy should you use? Should you start by confessing or keeping silent?

How will the actions of another participant affect your confessional decisions later on?

The prisoner dilemma is a complex game. To encourage cooperation, participants should punish each other for uncooperative behavior. But the previously described strategy of Jack and Jill's water cartel – that as long as the other defaults, one party defaults forever – is not forgiven.

In a game that has been repeated many times, it may be more desirable to allow participants to return to the outcome of the cooperation after a period of non-cooperation.

To illustrate which strategy is best, political scientist Robert? Robert Axelrod played a match. People enter the game through a computer program designed to repeatedly play the prisoner's dilemma.

Each program in which the game is played corresponds to all the others. The one who gets the procedure with the fewest total years in prison is the "winner".

The winner results in a simple strategy known as a pay-for-one. According to the report and the report, the participants should start with the cooperation, and then the other participant should do what he or she did the last time. Therefore, the participants must cooperate until the other party breaches the contract; He defaulted until the other party re-joined the game.

In other words, the strategy starts with friendship, punishes unfriendly participants, and, if the other person changes, gives forgiveness. To Axelrod's surprise, this simple strategy is better than all the more complex strategies that people lose.

This is to illustrate that the competition between two oligopolies in business does not necessarily produce the result of maximizing the utility of both.

To solve it, 1, make a single game into a multiple game, and gradually the two sides of the game will choose the most favorable outcome; 2. Make the threat credible, where one party threatens the other party to make a certain choice and convince the other party that the result of the breach is not good for itself.

The prisoner's conundrum is a well-known economic model that explains why short-sightedly profit-seeking leads to unfavorable outcomes for all.