Game Theory: The Prisoner's Dilemma And Nash Equi

Game Theory: The prisoner’s dilemma and the Nash Equilibrium

Two woman Ana and Kara are both arrested at different times for the same type of crime: stealing a car. Both crimes were done individually and the district attorney goes to see them in different interrogation rooms and tells them that they were both caught red handed and that they are both getting two years. While observing their profiles he notices that they fit the profile of two characters that committed a more serious offence: carrying out an armed robbery a few weeks before, but he realizes that he has no hard evidence and needs a confession to sentence them.

Options for both prisoners

Globally optimal scenario

Regardless of the globally optimal scenario

We reassign their values to be for Ana:
W: 8 X: 5 Y: 2 Z: 1
Choosing to confess ensures that a player will receive either A or C. Choosing to keep quiet in contrast ensures B or D. The number chosen to represent were chosen arbitrarily so that W>X>Y>Z, therefore confessing is always the better option.
The use of this inequality stipulated, yields what is known as a "Nash Equilibrium," as existing in a game if both players are aware of the reward structure, each is knowledgeable of his or her opponent's options, and as a consequence makes a rational decision considering those options, there is always one decision that is better than the other. In the prisoner's dilemma in which W>X>Y>Z, both players confessing is a Nash Equilibrium as long as W exceeds X which will be proved