Game Theory Applied to the Death Penalty - Appunti

B.

In case of Life Imprisonment, the Exp(L) of their conviction will be

higher because they will only retain some rights while serving

without the possibility of regaining freedom, which is 90. The

two-by-two matrix, then, will be (the red color indicates the choice

of A; the blue color indicates the choices of B):

A A

• Attempt Murder

Attempt ↑ 60 , 60← 70 , 90

B Murder 90 , 70 ↑ 67.5, 67.5

←

This case also has two Nash Equilibria as solution. In fact, even if

the Exp(L) is higher, the players will still decide to kill if the other

player decides to kill, and to attempt if the other player decides to

attempt.

Death Penalty

C.

The death penalty means for each player the loss of every right

they could have, meaning no possibility to retain further rights after

the serving the penalty. In this case, then, the Exp(L) is the highest

possible and will be of the maximum amount: 120. The two-by-two

matrix this time would have some differences from the other two

cases previously examined (the red color indicates the choice of A;

the blue color indicates the choices of B):

A

Attempt Murder

•

Attempt ← 80 , 80 ↑ ← 90 , 120

Murder 120, 90 ↑ ← 90 , 90 ↑

B

As we can see, now:

If B decides to attempt B will decide to attempt as well,

- because 80 is lower than 120;

If B decides to murder, A will be indifferent between

- attempting and murdering;

If A decides to attempt, B will decide to attempt as well,

- because 80 lower than 120;

If A decides to murder, for B the choice between attempting or

- murdering will be indifferent.