## Prisoner's Dilemma

The fundamental theory of two person games is that every zero sum game with mixed strategies has a unique value that is the same for both players. If the game is not a zero sum game, some solutions will yield more profit than others. Cooperation becomes a profitable option and the the solution may not be unique.
The 'prisoner's dilemma' is a two person, non zero sum game. Two players A and B are jointly accused of a crime. They are separated and separately interviewed. They are presented with the following alternatives. If you both plead guilty, you will both be detained for five years. If one of you denies complicity while the other admits it, the one who admits his guilt will be freed, and the one who denies complicity will be detained for ten years. If you both deny complicity, you will be detained for two years.
Are you innocent or guilty?
The payoff matrix for A is
 A\B Guilty Innocent Guilty -5 0 Innocent -10 -2
The payoff matrix for B is
 A\B Guilty Innocent Guilty -5 -10 Innocent 0 -2
From A's point of view the guilty strategy dominates the innocence strategy, so if he were rational he would admit he and B committed the crime, and the same is true for B. This combination of strategies is not optimal. If both pleaded innocence, they would have served only two years each.