Eli5: Why is Prisoners Dilemma considered a Dilemma?
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There are two or more choices, and all possible choices carry a risk (with consequences). The act of making a choice means you’re accepting the risk and consequences.
It’s a dilemma because there is no risk-free choice.
“The Prisoner’s Dilemma”, as we know it, is a game analyzed in game theory. It isn’t a “Dilemma” in the everyday sense of the word – just a thought experiment. It was originally created in the 50s. It was a guy called Albert W. Tucker who named it the “prisoner’s dilemma”.
It is:
>Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with the other. The police admit they don’t have enough evidence to convict the pair on the principal charge.
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>They plan to sentence both to a year in prison on a lesser charge. Simultaneously, the police offer each prisoner a Faustian bargain. If he testifies against his partner, he will go free while the partner will get three years in prison on the main charge. Oh, yes, there is a catch … If both prisoners testify against each other, both will be sentenced to two years in jail.
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>The prisoners are given a little time to think this over, but in no case may either learn what the other has decided until he has irrevocably made his decision. Each is informed that the other prisoner is being offered the very same deal. Each prisoner is concerned only with his own welfare—with minimizing his own prison sentence.
There are essentially 4 possible outcomes.
* If prisoner A and prisoner B both remain silent, they will each serve one year in prison.
* If A testifies against B but B remains silent, A will be set free while B serves three years in prison.
* If A remains silent but B testifies against A, A will serve three years in prison and B will be set free.
* If A and B testify against each other, they will each serve two years.
It creates a situation where loyalty is inherently an irrational viewpoint. The rational decision would be to betray your accomplice but several studies have found a “bias” towards cooporation, rather than the obvious choice.
The ***prisoners*** are facing a ***dilemma*** because they need to make a decision with imperfect information.
They can wonder about what other prisoners are likely to do, but then they have to make a decision without knowing for sure.
We’ve known for a while that there IS a solution to the prisoner’s dilemma, so in that sense the hypothetical prisoner doesn’t really face a “dilemma” because there is one clearly superior choice. The simplest answer is that the guy who came up with it named it that, and the name stuck.
But there are some reasons to still think of the scenario as a dilemma:
1. The prisoner is trying to minimize a bad thing. There is no option where he comes out better than the scenario where he doesn’t play at all. One might say that being put in such a position always poses a dilemma, even if one choice is less-bad than the other.
2. The solution to the prisoner’s dilemma is not intuitive, so the dilemma may be the challenge of figuring out what to do, or possibly the despair of a prisoner who can’t figure it out.
So there are those math problems when you have to give the result of 5+5, but instead of asking 5+5, they tell a story. Like, Johnny had 5 apples, and later his friend Jim gave him another 5 apples, how many apples does Johnny have now. You can give this story a title, like Johnny’s apples, but in the end it’s 5+5.
The prisoner’s dilemma has this dilemma in the title because the story is given as a dilemma of a person. Otherwise in the core it’s just the following math: two actors act simultaneously, they are incentivised to act selfish as asymmetric selfishness awards the best individual score for the selfish and the individual worst score to the cooperative actor. But if they both act selfish, the system punishes them with the worst total score, while the best system level total score is gained with symmetrical cooperation.
The numerical values (0,1, 8, 12 in the original) are arbitrary and can change as long as:
– the symmetrical cooperation (1 penalty) gives you worse personal score than you can reach if you’re on the winning end of asymmetry (0 penalty).
– the total system value of symmetrical cooperation is less than any other total value (1+1=2 vs 12 vs 16)
– the symmetrical non-cooperation (8) gives you personally better than the loser end of asymmetry (12).
– and the symmetrical non-cooperation gives the worse total value (16 vs 12 vs 2).
If these are all met in a two-actor situation, you have a prisoner’s dilemma.
Another way to think about it is if you imagine two rival countries (A and B) who don’t get along and might fight. Each one can build weapons or not build them. They can jointly agree to not arm (cooperate) or they both can arm. It’s better economically if they both don’t arm since presumably each can use the money for something better. But the very best thing is if A can convince B to not arm and then cheat by arming. But if B finds out and then arms both end up worse than if they cooperated. So in simple terms things are better by cooperating but are best if you cheat while the other guy cooperates. BTW I got a PhD in mathematical game theory.
And I think one of then can get shot?
The “Di” in dilemma means two. Dilemma means a situation two choices. Usually a dilemma is a tough choice.
To win the game a player has to betray a friend or accept they’re going to jail.
A prisonner’s dilemma is a tough choice because if both players do cooperate both go to jail and neither go free, but if either defects someone will serve more time in jail than if they both cooperate. Being selfish is the best strategy only if a player defects on a cooperating player.
A prisoner’s dilemma involves two players with two choices each. There are four possible results from the choices of the two players, but each player only has two options to chose from. Di = two.
The first option is to cooperate. That means work together. If both players cooperate, they both receive the 2nd best outcome.
The second option is to defect. That means to cheat or betray. If one player defects while the other player cooperates, the defecting player receives the 1st best outcome. The cooperating player in a game with a defecting player receives the 4th best (the worst) outcome.
If both players defect, both receive the 3rd best outcome.
The choice is a dilemma because the best scenario for a player is to defect while the other player cooperates. But if both players cooperate, each player does better than if both players defect. Cooperation has the highest risk and only the 2nd best reward. That’s why it’s a dilemma, it’s a tough choice because defecting is always better than being the only player cooperating.
The dilemma comes from the way the game is structured so that each player making the best move for themselves results in both of them losing.
The best result is for both players to stay silent, but because of how expected value works, that outcome is impossible since the best move for each individual player is to snitch. That’s the “dilemma”. You’re forced to “lose” the game because it’s the only correct move to make.
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