Introduction to Game Theory

Published 14. Oct 2016 by Sam Briesemeister.

Game theory is the science of understanding behavior among multiple decision-makers in any system of rules.

The Prisoners’ Dilemma

In the classic Prisoner’s Dilemna, two suspects are asked to divulge incriminating information about the other in exchange for a reduced penalty. Each has the option of remaining silent. There’s no communication permitted between the suspects: they must act speculatively, judging the other suspect’s motives and character, while evaluating their own subjective risk/reward model.

This is usually modeled as a matrix:

  B: divulge B: silent
A: divulge 2x each B: 3x; A: 0
A: silent B: 0; A: 3x 1x each
  • If both divulge, they each get 2 years imprisonment as penalty.
  • If just one divulges, he receives no penalty, and the other receives 3 years.
  • If both remain silent, both receive a 1 year penalty.

Traditionally the interpretation of this exercise is that agents (i.e. suspects or prisoners) act based on subjective evaluation of the same matrix, albeit perhaps subconsciously, and that their behaviors can be influenced by altering the risk/reward model. Within that model though is a fundamental truth: choice can be manipulated by limiting information.

It’s worth noting that to the prison, in terms of total time served (in “man years”), the model looks like so:

  B: divulge B: silent
A: divulge 4 M.Y. 3 M.Y.
A: silent 3 M.Y. 2 M.Y.

Assuming the prison somehow benefits from maximizing total penalties, it’s in the prison’s interest to motivate each suspect to divulge out of supposed self- interest. Presuming the suspects behavior is truly criminal (according to the prevailing social contract), one could argue that the whole society shares the interests of the prison, and therefore maximizing total time served by both suspects is advantageous.

A worthy question though: what role would private prisons play in this dynamic?