Grade Level
The Prisoner’s Dilemma is a math problem that incorporates ideas from game theory. It aims to mathematically represent behavior in a situation where an individual's success in making choices depends on the choices of others. Because it does not have a “standard probability”, and instead, it involves recursive choices, it’s recommended that the game targets high school students. Less complex versions of the game, however, can be played and understood by students with a basic grasp of probability and deductive logic skills.
The Problem
Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal. If one testifies for the prosecution against the other (“betrays”) and the other remains silent (“cooperates”), the betrayer goes free and the silent accomplice receives the full twenty-year sentence. If both remain silent, both prisoners are sentenced to only five years in jail for a minor charge. If each betrays the other, each receives a nine-year sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How would you act if you were one of the prisoners?
Materials List
• (100 x # of students in class) = pieces of candy needed (skittles/m&ms recommended)
• Screens made of poster board, cardboard, etc. that can stand between two desks
• Non-transparent containers
• Decks of 54 cards – one deck is needed for every 13 pairs of students
Required Setup
• Arrange student’ desks into pairs, face to face, creating an inner circle and an outer circle.
• Make sure a screen is between each pair of desks so that students cannot communicate with their “partners-in-crime”.
• Each student should be handed 100 pieces of candy, which represents “100 years of life”.
• A non-transparent container should be placed in the middle of each pair of desks, which symbolizes “years in prison”. Every skittle dropped into the container is a year in prison.
• Students in the inner circle should be handed a black and red card of even value (ie: black six of spades and red six of hearts).
• Students in the outer circle should be handed a black and red card of odd value (ie: black jack of clubs and red jack of diamonds).
• Emphasize the students should not communicate with anyone else and should not talk during the progression of the game.
