Prisoner’s Dilemma

One of the first games students of game theory learn is the Prisoner's Dilemma. It is a simple game that works well for various strategic situations. Once you see it and understand it, you'll see it everywhere.

The story goes like this. Two thieves planned to rob a store. As they approached the door, the police were arrested for trespassing. Police suspect the couple planned to rob the store, but they lack evidence to prove it a little. Therefore, they demand confessions to charge the suspect with more severe crimes. The interrogator will suspect Separate people and tell them:

"We are charging you with trespassing, which will land you in jail for a month. I know you intended to rob the store, but I can't prove it without your testimony. Come clean now, and I will dismiss your trespassing charge." Set yourself free. Your friend will be charged with attempted robbery and faces 12 months in prison. I am making the same offer for your friend. If you both plead guilty, your testimony will no longer be of value to both of you. He will be sentenced to eight months in prison ."

Both players are selfish and want to minimize their jail time. What should they do?

Using a revenue matrix allows us to condense all the information into an easy-to-analyze chart:

Player 1's available strategies are rows (Silence or Confession); their corresponding payoff is the first number in each cell. Player 2's available strategies are the columns, and their corresponding payoffs are the second numbers in the cells.

quiet: silence; confess: confess; the blue number is the profit of player 1, and the red number is the profit of player 2;

-1: Imprisonment for one month; -8: Imprisonment for 8 months ; -12: Imprisonment for 12 months ; 0: Acquittal;

●Hypothesis and conclusion:

We assume that both players have a preference to minimize their jail time

We assume that both players are selfish (i.e., they don't care about the fate of their friends)

We assume there is only one interaction

We assume players cannot interact and plan their reactions in advance

These assumptions lead to a suboptimal outcome in the game ( confess, confess), which is (-8, -8). We can see that if both players remain silent, they will receive less jail time. It is an unstable equilibrium. If both parties believe the other will remain silent, they will confess.

Therefore ( confess, confess) is the only Nash equilibrium. A Nash equilibrium is a state in a game where no player wants to deviate from their strategy, given what the other players are doing.

However, if both players cooperate and keep quiet, they will achieve better results. It is an essential conclusion because it shows us that two people may not cooperate even though it seems the Party's best strategy.

Breaking through the prisoner's dilemma is significant to the broader society and ORIGIN. We are often told that in a capitalist economy, individuals only care about their self-interest, so selfish and competitive behavior is the norm, while cooperation is the best way to win.