Question

Explain the Prisoner’s Dilemma. Give a numerical example and show how each player would make decisions.

Answer 1

Prisoner's Dilemma is a classic two person game in game theory. It shows us that two rational individuals might not cooperate even when it is best for them to cooperate. It shows how two parties acting in their own self interest does not usually lead to the optimal outcome.

Example-

The police arrests two suspects and interrogates them. They are kept in separate rooms and cannot communicate. Each prisoner can either confess of remain silent. Pay offs in this game are the number of years in prison, based on the choices they make.

If both of them confesses, both will serve two years in jail.

If prisoner 1 confesses and prisoner 2 remain silent, prisoner one goes free and prisoner 2 will get 2 years jail term. And vice versa.

If both remains silent, both will serve 1 year in jail

Given this senario, the dominant strategy for both of them is to confess even though the optimal outcome is to remain silent and serve 1 year jail term. Since, both of them act in their own best interest, they fail to make a mutually beneficial choice.

		Prisoner 2
		Confess	Remain silent
Prisoner 1	Confess	3,3	0,4
	Remain silent	4,1	2,2

If prisoner 1 confesses, prisoner 2 also confess as 3 yr jail term is better than 4 yr jail term.

If prisoner 1 remain silent, prisoner 2 also confess as 1 yr jail term is better than 2 yr jail term.

If prisoner 2 confesses, prisoner 1 also confess as 3 yr jail term is better than 4 yr jail term.

If prisoner 2 remain silent, prisoner 1 also confess as 1 yr jail term is better than 2 yr jail term.

So, the Nash equilibrium is for both players to confess and serve 3 years jail term, even though we can see that if both remained silent they would face 2 years jail term.

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