The Prisoner's Dilemma
Two individuals are arrested and imprisoned in different and isolated cells. The prosecutor suspects that they have participated in a bank robbery. The crime is punished with 10 years in jail, but he cannot prove it. The only evidence is related to illegal possession of weapons, a crime which is punished with 2 years in jail. In order to get incriminatory information from the prisoners, the prosecutor promises to each one of them to reduce their final sentence to half if they provide the proofs that will inculpate the other prisoner.
Given those conditions, what is the best decision that a prisoner can take?
Possible outcomes
Let's have a look into this problem. First of all, and in sake of simplicity, I will name the prisoners as A and B. We can find that there are only four possible outcomes in this story:
1) Prisoner A remains silent and prisoner B as well --> Both of them get a 2 years sentence for illegal possesion of weapons.
2) Prisoner A remains silent, but prisoner B betrays A --> Prisoner A gets a 10 years sentence and prisoner B gets a 2 year sentence that is then reduced by half in regard of his cooperation, so he stays only 1 year in jail.
3) Prisoner A betrays B and prisoner B remains silent --> Prisoner A stays 1 year in jail and B stays 10 years.
4) Prisoner A betrays B and prisoner B betrays A --> Both of them get in principle a 10 year sentence, but the sentences are reduced to 5 years because of their cooperation.
The story seems to be just an entertaining riddle. But it happened to be the starting point in a very interesting quest to explain certain components of human morality such as altruism, solidarity, trustfulness and forgiveness.I will stop here by now. But in future posts I will keep commenting on this issue.
1 comentario:
Hmmm, I want to comment on this... the problem is, I already knew the story and discussed it with Roger before. So I'm kinda biased :P
Nevertheless, I will post what I think. In the end, one can analize all the permutations and gamble based on the odds. I'm not gonna dwell on that part, since anybody can run the numbers by themselves :P
I'm just gonna add other aspects to take into account. First of all, what kind of relationship is there among the two thieves? If they are good friends who can trust each other, then they may be willing to risk not saying absolutely anything (2 years each. No significant crimilar records, etc. Everybody happy). The may have some sort of code regarding betrayal. If that's the case, one year in prison may be more than enough for the betrayer to get killed by other thieves for breaking the code. All that is needed is to spread the word and that guy will be paying way more than the price of 10 years in prison.
Now, if there isn't such code and they were just random thieves who teamed up to commit a robbery, then by all means, speaking up is the way to go since you reduce the possible sentence you are gonna end up paying.
One last thing is... I think it's rather difficult to provide evidence about the robbery without incriminating yourself in the process, and what one usually sees in the movies is that both end up paying for the crime :P so there would be no 1-year way out for the one who betrays the other. To top it off, in real life sitations, the incriminated guy would probably supply evidence against his partner as soon as he finds out he has been betrayed. And you don't really ask the incriminated guy to simply shut up for the rest of his life, do you? :P
I'm sure the jury would be more than happy to put the betrayer in prison for 5 years instead of 1.
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