Film Analysis: The Prisoner's Dilemma

Jullian Karel Androkae

DP1 Math HL

The Prisoner’s dilemma

Mathematical Exploration

Table of Contents Introduction

The prisoner’s dilemma got me intrigued since the very first time I encountered it a few years ago while trying to learn more about how my favorite TV shows worked, especially “Brain Games” broadcasted on National Geographic Channel. These games often applied game theory to understand human and social behavior. However, my interest about this model of game theory multiplied after encountering a brilliant short movie realized by the French video maker Wil Aime, entitled “Le dilemme du prisonnier” (in English ‘The prisoner’s dilemma’). The video was described with the following question: “If you committed a murder, which one of your friends would cover you?” This film presented a version of the prisoner’s dilemma where 4

While also represented and studied in economics or philosophy, game theory takes a specific mathematical aspect. John von Neumann and Oskar Morgenstern are the first to develop it in 1944, in “The Theory of Games and Economic Behavior” because classical mathematics (often used to describe Physics for instance) revealed being inefficient to describe and explain Economics. To them, it was closer to a strategic game.

Therefore, Game theory is a relatively recent branch of mathematics that studies situations in which players (sometimes called parties) make independent decisions and considering the other one possible choice while building their strategy. The decisions of the players that lead to an optimal outcome represent a solution to the game. One important part of game theory is that the players’ choices influence the outcome of the game, putting decision making in the heart of game theory. In that optic, game theory surpasses the study of probabilities.

The prisoner’s