Is the Prisoners' Dilemma Always a Nash Equilibrium? Is a Nash Equilibrium Always a Prisoners' Dilemma?

Question 8 - Is the prisoners' dilemma always a Nash equilibrium? Is a Nash equilibrium always a prisoners' dilemma? Explain.

The prisoners' dilemma is an example of a Nash Equilibrium. However, a Nash Equilibrium does not have to always be a Prisoners' Dilemma. There can be more than one Nash equilibrium in any game theory (as shown in table 1.1). To find a Nash Equilibrium, we look for the highest number in a certain column, the check to see if the number paired to it is also the maximum number in the corresponding row. In the table we can see that there are 3 Nash Equilibria.

Table 1.1 – Nash Equilibria are in bold

Option A Option B Option C

Option A 0, 0 25, 40 5, 10

Option B 40, 25 0, 0 5, 15

Option C 10, 5 15, 5 10, 10

Prisoners' Dilemma:

In the situation of a prisoners dilemma as shown in table 1.2, there is only one Nash Equilibrium that occurs when both parties defect.

Table 1.2

Cooperate Defect

Cooperate 3, 3 0, 5

Defect 5, 0 1, 1

To re-address the question; in the situation of a prisoners' dilemma, there will be one combination of choices which represents a Nash Equilibrium. A prisoner's dilemma is when there is a Nash equilibrium, but one at which it is not the best outcome.

Additional Problems

1. Consider your prior work situation. In the context of that situation, answer the following questions to the best of your ability:

a. Who are your customers? (Do they have any distinguishing features? That is to say, are they old or young, rich or poor, foreign or domestic, married or single, etc.?)

When working for Microsoft technical support helpline, my customers would call with problems concerning their Windows PC. They were international (usually from USA) and typically they may be older, not so experienced with technical issues. I cannot say whether they were married or single, but it was generally women who called in (perhaps on behalf of their husbands). I believe they were people from all socio-economic groups, excluding the very poor.

b. Are your customers sensitive to the price they had to pay for the product or service you sell? What leads you to that conclusion?

I believe the customers were relatively immune to the price. They had a problem and it needed to be fixed,