Wednesday, May 8, 2013

The Prisoner's Dilemma

Raise your virtual hands: how many of you have heard about the prisoner's dilemma? The prisoner's dilemma is a classic example of a game studied in game theory, economics, psychology and other assorted disciplines. I first heard about it in a university course a few years ago. Here is how it works. As a thought experiment, imagine the following situation, and put yourself in the position of the participants:

Two members of a criminal gang are arrested. They are interrogated separately. The police admit that they do not have enough evidence to convict the criminals on the primary charge. They only have evidence to sentence both to a year in prison for a lesser charge. However, the police offer each criminal a deal: if he testifies against his partner, he will go free and the partner will get three years in prison. If he stays silent and the partner testifies, the partner will go free and he will get three years. And if both criminals end up testifying against each other, they will each get two years in prison.

It's an intriguing and ominous situation to imagine yourself in. Do you decide to stay silent? If you do and your partner does as well, you will both get one year in prison. Not so bad under the circumstances. But if your partner testifies while you stay silent, you will get three years, the harshest penalty possible, while your partner goes free. So, should you play along and testify? If you do and your partner does as well, you will both get two years. And of course, there is always the possibility that your partner will remain silent while you testify, in which case he is the one getting the harsh three year penalty and you go free...

What makes the prisoner's dilemma so interesting for game theory is that it rewards betrayal. If your partner stays silent, then betraying him means a better outcome for you in terms of prison time than staying silent (you go free instead of getting one year). And if he testifies against you, then testifying against him also gives you a better outcome than staying silent (you get two years instead of three). In both cases, betrayal rewards more than staying silent. So, a rational individual whose only goal is to minimize prison time for himself should always choose betrayal over staying silent regardless of what their partner does.

Of course, people are not always so coldly rational, and there might be other factors that come into play. One or both of the prisoners might have motivations that to them are more important than simply minimizing prison time for themselves. For instance, a prisoner might feel an overriding sense of loyalty to their partner, or he might be bound by a strong personal code of honour. This might be rare among petty criminals, who usually are not the most loyal or honourable types, but it would be a lot more likely among freedom fighters, political activists and similarly idealistic groups.

I can't really imagine Kaelah or myself embarking on a life of crime. We both have too strong a moral compass for that, and besides, crime almost never pays off for the criminals in the long run - they are far more likely to get arrested or killed than to enjoy a long successful career. However, I can quite easily picture a fantasy of us as political activists who have been arrested by a dictatorial regime. Would I betray Kaelah if the regime offered me such a deal? Never. Because she is my loved one and as a matter of general principle, I would refuse to testify. And I would have the utmost confidence that she would do the same.

But let's say the partner who was arrested with you is not your loved one or a close friend, but a mere acquaintance. Let's say that you are not political activists, that you have really done something bad, which he talked you into and which you now regret. Let's also say that you are not quite sure of the loyalty of that acquaintance, whom you do not know all that well. Would it not be tempting, under this set of circumstances, to testify? Even if you have a strong personal code that would normally forbid you from doing so, you would probably at least take the option into consideration. Especially if we replace the linear set of penalties from the canonical prisoner's dilemma, one, two or three years in prison, with a more exponential progression, like one, three and ten years. Can you really afford to risk staying silent while your "partner" talks, which will get you a draconian ten years in the can? If you talk, the worst that can happen to you is three years if he talks as well. And if he stays silent, you go free...

I'm sure you already guessed why I brought up the subject in the first place. Anyone with an inclination for BDSM can see that there is potential for a kinky scenario here. One could play out the spanko version of the prisoner's dilemma and replace the prison sentences with corporal punishment. Flogger, paddle, cane? Take your pick. If both prisoners stay silent, they get ten strokes each. If one talks and the other stays silent, one goes free while the other gets a harsh thirty strokes. Tough luck! And if both talk, twenty strokes each. Or you could raise the stakes and use a more exponential progression of numbers, like six, twenty and sixty strokes. That should be interesting, especially when you play it with canes.

Scenarios like that are not everyone's cup of tea, but for people who like a bit of edginess in their kink, the prisoner's dilemma could be quite a treat. And there is plenty of video material here - frankly, I am surprised that Bars and Stripes have never done a take of their own on this game theory classic. It would seem tailor-made for them.

What about you? Would the prisoner's dilemma scenario catch your interest? Have you ever played it out for real? I know of at least one group of spanko friends who have (with both "prisoners" ratting the other out almost immediately). And most intriguingly, what would you do as a participant in the scenario, if the partner was a) a good friend or loved one, b) someone you don't know well, but are inclined to trust, and c) someone you don't know well and about whose loyalty you have doubts?


Anonymous said...

Have you ever seen the movie Goodfellas. Robert De Niro tells Ray Liotta the rule of the streets:

"You keep your mouth shut, and don't rat on your friends."

In my case, I would be silent. I am a very honest person, but I would never tell on a friend.

I could see this dilemma scene playing out in an interrogation scene with two bottoms and a top. I imagine it would be a very intense scene.


Fenris said...

I heard about this before. It is quite interesting as a thought experiment as well as scenario in a kinky context.

As a real world scenario, I think that the outcome would depend, as you already pointed out, on how well you know your partner in crime, whether it was a crime solely committed because of pure egoism or because of an underlying ideological purpose and, last but not least, whether the prisoners are submitted to torture. I guess that in this case, you will soon tell yourself that your partner has already given in so that there is no use in staying silent.
Honestly, I am not sure how I would behave in a real world scenario. Of course, I hope that I would remain firm and not rat out a loved one or loyal partner, especially in case we were political prisoners and not "mundane" criminals.
You probably know the ending of "Nineteen Eighty-Four" by Orwell.

"Under the spreading chestnut tree
I sold you and you sold me"

Not really romantic, but quite realistic considering the circumstances described in the novel.

Maybe you have heard about another interesting thought experiment, called the truel, i.e. a duel with three shooters involved. Interestingly, if deliberate missing is allowed and you are the one to shoot first, it is a good idea to miss because you do not pose a threat anymore so that luckily, the two remaining duelists will not target you...

Ludwig said...

@ joeyred51: I've seen Goodfellas many times. It's a classic. Of course, it ends with Henry Hill (played by Ray Liotta) ratting on his friends and entering the witness protection program, which goes to show that friendship has a short life span in the world of organized crime when people face the threat of long prison sentences.

@ Fenris: Yes, when I wrote that I would "never" betray Kaelah with such a deal, I was assuming a situation where I am not submitted to torture. I can't say how I would hold up under torture. I don't think anyone can.

I've read the book Nineteen Eighty-Four and seen the famous movie version with John Hurt and Richard Burton. I think the movie is even more depressing than the book - it is one of the most depressing movies I know! Well worth seeing, though.

Thank you for bringing up the "truel" thought experiment. I had not heard about that before.

Phew said...

Perhaps one interesting scenario might be the Iterated Prisoner's Dilemma, in which the game is not just played once, but dozens of times in succession, with the same players and reduced penalties (e.g., three strokes, two, and one).
This leaves room for reacting to the other's strategy, by rewarding your partner for previous loyalties and retaliating for betrayals. Always betraying is no more the most rational option, because your partner can get revenge on you in successive rounds.
It has been found that one of the best strategies (dubbed "Tit for Tat") is in fact just reacting to your partner's choice in the immediately previous round, and "paying him back with the same coin". Richard Dawkins' "The Selfish Gene" has a nice illustration of this dilemma, tied to the advantages of cooperative behaviour in society from the evolutionary point of view.
Do you think this would play out at all in a real life kinky game?

On an unrelated note, I have always found the final chapters of Nineteen Eighty-Four to be very kinky.

Also: 4 year long-time reader delurking here. Hello!

Respecting Mistress said...

Wow that's a very interesting idea. But what if it were you and Kaelah and the strokes started at 24 so there was real severity here and you knew the caner would spare neither of you? Would you both protect each other and keep silent to suffer the 24 each or would you testify against her? What if there were an option to admit to the crime yourself and take extra punishment to save Kaelah? Would you be prepared to do this for here - or her do it for you? And what if there were a third or more person(s) added to the scenario? The situation would become so achingly impossible to decide what course for the best. What a fascinating concept. I'm generally only interested in corporal punishment used as a corrective measure for real faults. But this idea really excites.

Phew said...

...And now I realise that everything I wrote is already on the main Wikipedia page for the Prisoner's Dilemma, and probably everybody knew about that already. I apologise.
Darn Wikipedia, you can't contribute anything useful anymore.

Ludwig said...

@ Phew: Hello, and thank you for your comment. It's always great to see long-time readers delurking.

Yes, I have heard about the iterated version of the prisoner's dilemma. I thought about mentioning it in the post, but did not want to make it longer than it already was. The iteration makes the game even more interesting, of course, because it allows the participants to react to each other's decisions.

Would the "tit for tat" strategy play out in a real life kinky game? I have no idea. One would have to try it out for real, and observe the results. But because it is such an obvious strategy and appears fair, in a way, it stands to reason that quite a few people would probably use it.

@ Respecting Mistress: In the scenario you describe, I would just keep silent and take the 24 strokes. I would neither testify against Kaelah nor volunteer to extra punishment to save her - we are both switches and we have a fully equal, eye-to-eye relationship, so I don't do the "knight on a white horse in shining armour" thing. Kaelah would not want me to! We would both keep silent and take the strokes.

Kaelah said...

In my opinion the prisoner's dilemma scenario a very interesting (thought) experiment, the version with one round as well as the iterated variant!

I have to admit that I have no idea how I would react in the real situation, though. Suffering from claustrophobia, even the thought of having to spend more than a few minutes in a small enclosed space such as a prison cell is incredibly scary for me. I wished I could say I am absolutely sure that I would do the right thing (from an ethical point of view) and remain silent, at least with a loved one being involved. It would be a lie if I did, though. Of course I have a clear idea of how I would want to react from an ethical point of view, but I don't know what would really happen if I panicked. Not even to mention the possibility of being tortured! Well, I guess I better stay away from committing or getting somehow involved in any criminal offense...

As for the kinky scenario, I am not sure whether I would like to try that one out for real, either, at least as a bottom, because it sounds too much like a dark scenario for me. If I did, though, I definitely wouldn't testify against the other prisoner, no matter how much I would or wouldn't like and trust that person and how severe the punishment would be (I would only participate if the severity level were within my personal limits, anyway). The reason is very simple: It would definitely be much easier for me to endure a harsher spanking while having the moral high ground than enduring a physically less challenging spanking while feeling like a traitor and loser. In this context the idea of offering to take the punishment for another person also holds some appeal because it fits to my heroine fantasies. I guess I would not do that if you were the other person, though, Ludwig, for the reason you already mentioned in your comment. I know that you wouldn't want me to save you and that it would make you feel uncomfortable (just as it would make me feel if you jumped in for me, maybe unless it were a scripted scene for a clip).

@ Phew:
Welcome and thank you very much for delurking! I think almost everything can be found somewhere on Wikipedia, so don't worry about that. :-)

! said...

Coming back out of lurking again, to say that this would be an excellent scenario for me to play out. I would probably betray my partner in every circumstance and expect him/her to do the same for me, especially if the scene is being done with exponentially rising consequences and canes - it's the only logical thing to do.

Phew said...

@ Ludwig and Kaelah:
Thank you very much to you both for welcoming me.

Lea said...

I have never played out a scenario like this and don't know if I would. Generally, I have learned that silence can be the best defense.