Two accomplices (P1 and P2) who have committed a crime have been charged by the state.
Let C denote "cooperate" (when the accomplice cooperates with his partner by not turning state witness) and D denote "defy" (when the accomplice defies his partner by turning state witness).
The accomplices' possible actions, together with the consequences of these actions, is summarised in the table below. The pair (1,10) denotes that P1 gets a 1 year sentence and P2 gets a 10 year sentence.
[table="width: 500, class: grid"]
[tr]
[td][/td]
[td]P2: C[/td]
[td]P2: D[/td]
[/tr]
[tr]
[td]P1: C[/td]
[td](3,3)[/td]
[td](10,1)[/td]
[/tr]
[tr]
[td]P1: D[/td]
[td](1,10)[/td]
[td](8,8)[/td]
[/tr]
[/table]
Consider P1. He is better off by defying his accomplice. By defying his accomplice, he will get either a 1 year or 8 year sentence (depending on P2's action), while if he were to cooperate with his accomplice, he would get a 3 year or 10 year sentence respectively.
Likewise P2 is better of defying his accomplice.
Hence if both accomplices act rationally, they will both defy their accomplices.
The paradox is that this results in an 8 year sentence for both of them, even though the minimum sentence they both could potentially have received was 3 years each.
- A conviction of the full crime carries a 10 year sentence.
- The state has insufficient evidence to convict the accomplices of the full crime, but there is enough evidence to convict them on lesser charges. This lesser conviction carries a 3 year sentence.
- If exactly one of the accomplices becomes a state witness, he will get a reduced sentence of 1 year while the other accomplice will be convicted of the full crime and receive a 10 year sentence.
- If both accomplices admit guilt, they will both receive a slightly reduced sentence of 8 years.
Let C denote "cooperate" (when the accomplice cooperates with his partner by not turning state witness) and D denote "defy" (when the accomplice defies his partner by turning state witness).
The accomplices' possible actions, together with the consequences of these actions, is summarised in the table below. The pair (1,10) denotes that P1 gets a 1 year sentence and P2 gets a 10 year sentence.
[table="width: 500, class: grid"]
[tr]
[td][/td]
[td]P2: C[/td]
[td]P2: D[/td]
[/tr]
[tr]
[td]P1: C[/td]
[td](3,3)[/td]
[td](10,1)[/td]
[/tr]
[tr]
[td]P1: D[/td]
[td](1,10)[/td]
[td](8,8)[/td]
[/tr]
[/table]
Consider P1. He is better off by defying his accomplice. By defying his accomplice, he will get either a 1 year or 8 year sentence (depending on P2's action), while if he were to cooperate with his accomplice, he would get a 3 year or 10 year sentence respectively.
Likewise P2 is better of defying his accomplice.
Hence if both accomplices act rationally, they will both defy their accomplices.
The paradox is that this results in an 8 year sentence for both of them, even though the minimum sentence they both could potentially have received was 3 years each.
