Question

There are two prisoners: John and Matthew are suspected of committing a serious international financial crime. They each have a choice: they can either testify against each other or they can keep quiet. Consider the following payoff matrix:

Matthew

	Testify	Quiet
Testify	(3,3)	(0,10)
Quiet	(10,0)	(2,2)

John

if both John and Matthew testify simultaneously, they each get a moderate sentence of three years in prison, whereas if they both stay quiet, they each get a light sentence of 2 years. If either of the two prisoners testifies and the other remains quiet, the one that testifies get off free, by contrast the one that remains quiet gets the worst sentence in the game (10 years in jail at the Hague). Also, there is no binding contract in this game (non-cooperative game); thus, there is no guarantee that each prisoner will stay quiet. What is the dominant strategy equilibrium in this game? Is this equilibrium also a Nash equilibrium? Explain thoroughly the reasoning behind your answers.

Answer 1

If John testify, Matthew's best response is to stay testify (as 3 < 10).
If John stay quiet, Matthew's best response is to stay testify (0 < 2).

If Matthew testify, John's best response is to stay testify (as 3 < 10).
If Matthew stay quiet, John's best response is to stay testify (0 < 2).

Thus, the dominant strategy for both is to testify. This is because testifying always gives them lower term of jail irrespective of other prisoner's strategy, Thus, the dominant strategy equilibrium is (Testify, Testify) or (3,3).

Yes, this is also the Nash equilibrium because best response of both prisoners occur simultaneously when they choose to testify as when John testify, best response of Matthew is to testify and when Matthew testify, best response of John is to testify.