Game Theory in Action: What Would You Do in This Prisoner's Dilemma?

Game Theory and Its Application

I am starting the discussion on "Game Theory and its application." To start with, here is one puzzle. Please try to solve it:

Two suspects are arrested for a crime. The prisoners must decide whether to confess or not to confess. If both confess, both are sentenced to 3 months in jail. If both do not confess, then both will be sentenced to 1 month in jail. If one confesses and the other does not, then the confessor goes free (0 months in jail) and the non-confessor is sentenced to 9 months in jail.

What should each prisoner do?

More to come in the next post....

Regards,

Please provide the answer as I am working on a Game Theory project, and this would really help me understand the concept better.

This reminds me of a game called Golden Balls in the UK. Two contestants have to pick a ball for a jackpot prize. There is a jackpot of 60,000 pounds Sterling. If both choose "Split," they get half the jackpot prize. If one chooses "Split" and the other "Steal," the one that chose "Steal" gets all the money; and if both choose "Steal," then neither gets the money. What would you choose if you were a contestant?

Let's work on this. (Refer to my question) and also Simhan's problem can be solved by this method. We will make the payoff matrix as follows:

First Box:
Prisoner 1 and Prisoner 2
- Confess: Both get a 3-month sentence.

Second Box:
Prisoner 1 does not confess and Prisoner 2 confesses
- Prisoner 2 gets a 9-month sentence.

Third Box:
Prisoner 1 does not confess and Prisoner 2 confesses
- Prisoner 1 gets a 9-month sentence.

Box Four:
If both do not confess, they get only a 1-month sentence.

As per the Nash equilibrium, each player's predicted strategy is the best response to the predicted strategies of other players. Here, there is no incentive to deviate unilaterally. Strategically, it is stable and the best option. The probability is Box First: Both confess and get a 3-month sentence.

What do you think?

Regards,
Vinod Bidwaik

Hi All, In Simhan's question, the strategic self-enforcing option is the first box where both choices split. Any second opinion?

Regards, Vinod Bidwaik

Prisoner's Dilemma

What Vinod has written is called the "Prisoner's Dilemma." You can see more details at Prisoner's dilemma: Definition from Answers.com.

In the game I have cited, I have seen people share 90,000 pounds, as well as people stealing 1 pound. People who decide to split, just to see that they have lost, have said that they can sleep fully knowing that they did not lie or cheat.