What is the Prisoner's Dilemma?
Before diving headfirst into the realms of the Prisoner’s Dilemma, it’s important to understand what exactly a “game” is. Economists define “Games” as, typically non cooperative, how people interact in social settings. On a matrix, we have the choices or options available to both the players. Inside the matrix, we assign values based on how people feel about their choices in utility, essentially their various preferences in the given situation. These theories revolve around how we believe other people will behave in their situation, that is, how likely are they to be rational economic agents.
N-player games can be used to model large number of people, for example, in populations’ voting. Given the large number of people and players, agents must make decisions that they believe will be the best response no matter what the other players play. Uncertainty plagues the world that we, the players, live in, and it is this uncertainty that is at the very heart of game theory. Economic theory has always relied in rational people in rational situations, but the recent blooming field of game theory has now begun to account for some irrationality in human behaviour.
The Prisoners Dilemma it is a disturbing and mind-bending game where two or more people may betray the common good for individual gain – formally named by Albert W Tucker.
Two prisoners are given the choice to either stay silent or confess and betray their companion. Should both stay silent, they both spend 1 year in jail. If one confesses and the other doesn’t, the confessor will receive 0 years in jail while the one who doesn’t will spend 10 years in jail. If they both confess, both must spend 6 years in jail. If one were to map out these payoffs on a matrix, it would look shown in the above image.
On inspection, it is clear that the Player 1 are always better off confessing
o If Player 1 doesn’t confess and Player 2 does, their payoff would be -10. However, should they confess, their payoff would increase to -1 (fewer years in jail)
o If Player 1 doesn’t confess and Player doesn’t confess, their payoff will be -1. However, should they confess, their payoff would increase to 0. (No years in jail)
Hence, the “strictly dominant strategy” is to always confess, regardless of what the other player does. Given the symmetry in this Prisoners Dilemma, the same must be true for Player 2. If rational, both players will always confess leading to (-6, -6) output on the matrix. No player has any incentive to deviate so confess-confess is a Nash Equilibrium. However, at the bottom right, the (-1, -1) output seems to be a much better solution for both the prisoners, which is why the solution to this puzzle is so counterintuitive.
This striking fact about the Prisoner’s Dilemma game and the reason it exerts such fascination is that each player pursuing individually sensible behaviour leads to a miserable social outcome. The Nash equilibrium results in each player getting -6 utility, much less than the -1 utility each that they would get if neither confessed.