Prisoners
Dilemma
Prisoners Dilemma is an example of a 2 person game. A 2
person game is one in which only 2 parties can play. 2 men are caught spending
forged money and are arrested by the police. The detective believes these 2 men
not only spent the forged money but counterfeited it also. However he has no
evidence of this and so puts the men in different rooms and interrogates them
separately.
He tells them that if neither of them confess to being a
counterfeiter, then they will be charged with attempting to spend forged money
for which they would be sentenced to 1 year in prison. If they both confess to
being forgers then they would get a lenient sentence of only 4 years. If only
one of them confesses to forgery they will get off, but the other prisoner will
be get 10 years.
This information can be summarised into a pay-off matrix. The
outcomes are ordered as pairs (A,B).
|
|
B confesses |
B does not
confess |
|
A confesses |
(-4,-4) |
(0,-10) |
|
A does not
confess |
(-10,0) |
(-1,-1) |
In the payoff matrix above the results are negative as they
have something to lose, if they were positive it means they would be gaining
something. The
worst outcome for A if he confesses is 4 years, and if he doesn’t confess it is
10 years. Therefore he will confess. Similarly for B if he confesses the worst
outcome is that he gets 4 years were as if he didn’t confess he might get 10
years. Therefore he also looks to confess. Both A and B confess hence they both
get 4 years in prison.
|
