Prisoner's Dilemma: Solving Evil Warden's Brain Teaser

  • Thread starter Riposte
  • Start date
In summary, a group of four men were thrown into prison for jaywalking and sentenced to 80 years. However, the prison warden offers them a chance to go free by playing a brain teaser involving four lockers and keys. Each man must find the key that matches their cell number in one of the lockers, and they have a limited number of attempts. The prisoners, who happen to be brilliant mathematicians, strategize and realize their chances of winning are greater than 40%.
  • #1
Riposte
16
0
This brain teaser involves an evil prison warden with way too much time on his hands:

4 men are in thrown in prison for jaywalking. It must have been very blatant jaywalking, for their sentence is 80 years. Luckily for them, the warden is apparently not too attached to his job, because he offers them a chance to go free.

Each man will be taken into a room with 4 lockers in it. Inside each locker will be a key with a number on it. The man will first open one locker. If it contains the key corresponding to his cell, then he has succeeded. (The number on the key matches his cell number) If the locker does not contain his key, he must shut it and open one more locker. If this locker does not contain his key either, then he loses and the entire group fails. In order to be let free, each man must succeed in this task and find his key.

This is all done individually, each man will be taken to the room with all the lockers initially closed, and they can not leave each other signs or communicate in any way. The prisoners are put together and are given a half hour before the game begins to plan out their strategy.

Now clearly if these were run-of-the-mill criminals, they would have no strategy and be stuck with a 1/16 chance of freedom. However, these terrible jaywalkers happen to be brilliant mathematicians, and soon realize that their chances of winning are actually greater than 40%. What was their solution?
 
Physics news on Phys.org
  • #3
Oops, my bad. Is there any way to remove this thread?
 

FAQ: Prisoner's Dilemma: Solving Evil Warden's Brain Teaser

What is the Prisoner's Dilemma?

The Prisoner's Dilemma is a classic game theory scenario that involves two individuals who have been arrested and are being interrogated separately. Each person has two options: to confess and implicate the other person, or to stay silent. The outcomes of the game depend on the choices made by both individuals.

What is the "Evil Warden's Brain Teaser"?

The "Evil Warden's Brain Teaser" is a variant of the Prisoner's Dilemma in which there is an additional element - the warden. The warden offers the prisoners a deal: if one of them confesses and the other stays silent, the confessor will be set free and the other prisoner will serve a longer sentence. If both prisoners confess, they will both serve a shorter sentence. If both stay silent, they will both serve a longer sentence.

How do you solve the "Evil Warden's Brain Teaser"?

The most optimal solution for the prisoners is to both stay silent. This way, they avoid the risk of serving a longer sentence if one of them confesses and the other stays silent. It also ensures that they do not both serve a shorter sentence if they both confess. However, this solution relies on trust and cooperation between the prisoners, which can be difficult to achieve.

What does the Prisoner's Dilemma teach us?

The Prisoner's Dilemma highlights the tension between individual self-interest and collective benefit. It demonstrates that in certain situations, individuals may be better off cooperating and trusting each other rather than acting solely in their own self-interest. It also shows that the outcome of a situation can be greatly influenced by the choices and actions of all parties involved.

What are some real-life applications of the Prisoner's Dilemma?

The Prisoner's Dilemma has been used to study and understand various real-life situations, such as business negotiations, military conflicts, and environmental issues. It has also been applied in the fields of economics, psychology, and political science to analyze human decision-making and behavior. Additionally, the concept of the Prisoner's Dilemma has been used in game theory to develop strategies for situations where cooperation and trust are crucial.

Similar threads

Replies
20
Views
5K
Replies
2
Views
5K
Replies
84
Views
97K
Replies
7
Views
2K
Replies
2
Views
3K
Replies
10
Views
11K
Back
Top