Analysis of Prisoner's Dilemma

Analysis of the Prisoner's Dilemma

Recall the definition of Prisoner's Dilemma:

Two suspects in a crime are interviewed separately.

If they both confess, they will be sentenced to $3$ years in prison.

If only one of them confesses, he will be freed and used as a witness against the other, who will then receive a sentence of $4$ years.

If neither one confesses, they will both be sentenced for lesser crime, and each will spend $1$ year in prison.

		$\text B$
$\text A$		$\begin {array} {r {{|}} c {{|}} } & \text {Don't Confess} & \text {Confess} \\ \hline \text {Don't Confess} & -1, -1 & -4, 0 \\ \hline \text {Confess} & 0, -4 & -3, -3 \\ \hline \end {array}$

Analysis

Prisoner $A$ reasons as follows:

$B$ will either confess or not.

If he confesses, then if I also confess, I get $3$ years rather than $4$.

On the other hand, if $B$ keeps silent, then if I confess I go free, rather than serve $1$ year.

Therefore, whatever $B$ does, whether that be to confess or to keep silent, it is in my best interests to confess.

By using the same line of reasoning, prisoner $B$ also reaches the conclusion that it is also in his best interests to confess.

It follows that each prisoner will serve $3$ years, rather than the $1$ they will serve by both keeping silent.

Thus it is seen that by using careful and logical reasoning, both prisoners settle on a strategy which does not yield the best outcome for either of them.

Also see

• Results about the prisoner's dilemma can be found here.

Historical Note

The prisoner's dilemma was first posed by Merrill Meeks Flood and Melvin Dresher in $1950$.

The context in which they were working was the possibility of war using thermonuclear weapons.

It seemed that the defence analysts could reason themselves logically into starting a nuclear war.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): prisoner's dilemma