Game Theory 101 (#2): The Prisoner's Dilemma and Strict Dominance

Game Theory 101: The Complete Textbook on Amazon: www.amazon.com/Game-Theory-10...
gametheory101.com/courses/game...
Two prisoners are locked into separate interrogation rooms. The cops know they were trespassing and believe they were planning on robbing a store, but they lack sufficient evidence to charge them with the latter crime. Thus, they offer the prisoners the following deal:
If no one confesses, both will only be charged with trespassing and receive a sentence of one month. If one confesses while the other keeps quiet, the confessor will get to walk away free, while the one who kept quiet will be charged to the fullest extent of the law--twelve months in jail. Finally, if both confess, each criminal's testimony is less useful, and both will be locked up for eight months.
If each prisoner only want to minimize the amount of time he spends in jail, what should they do?
This lesson introduces the concept of strict dominance, which is a very useful tool for a game theorist.

[@HateSonneillon]

I guess I beat the odds in high school when my friend and I ended up in the security office. We were individually interrogated for something we did in class. We did not discuss any plans. They told each of us that we blamed the other. But we stuck to our story, aka the truth, and didn't change our story despite being lied to. Then we got off with only a 5 day suspension instead of an expulsion. Its funny/crazy how confident we were in getting out even though there was a real possibility that if we started blaming the other then neither of us would have finished high school.

[@vedantvasav9723]

what were y'all in the office for ?

[@HateSonneillon]

@@vedantvasav9723 It was in welding class, they had us practice making beads all the time and I wanted to do something else so I started welding pipes together, then my friend joined in and the teacher caught us and thought we were making weapons. We told them that I wanted to make art. They even called my mom and she said the same thing. It was pretty stupid in hindsight but that class kinda sucked. I was always super nervous and anxious to go to it. The only time I had fun was when we started welding the pipes.

[@EuroUser1]

@@HateSonneillon I don't know when and where it was. But, in present-day Spain, it's essentially impossible to prevent a person from finishing high-school; specially on the basis of a tricky interrogation.

[@TheYoutubeUser69]

@@HateSonneillon bro what the gfuck is wrong with american schools. welding classß making weapons? arent yall shooting each other on a daily basis. who the fuck uses a stick when every mom and dead si sporting a fucking handgun in your country. the cognitive dissonance is out of control lol

[@Lrripper]

Yup, because humans can develop relationships that will defy the models

[@gabrielkumontoy1053]

You're A GIFT from the heavens. Much better explained than my lecturer, can't thank you enough.

[@jamirhussain7678]

Gabriel Kumontoy the same time as the one you

[@dirtperson5234]

this doesn't take account to the fact that snitches get stitches.

[@Gametheory101]

Then you have "stag hunt" preferences, which are covered a couple of videos from now. Remember: payoffs represent a player's preference--they do not mean a player MUST have those preferences. If you change the inputs of the game, you shouldn't be surprised if the outputs change as well. So if you have more cooperative preferences, it is possible to achieve cooperation.

[@DeepakSingh-ji3zo]

Excellent Explanation!! I saw 10 videos before this and it was still confusing. This is crystal clear. Pure Gold!! Keep up the good work!

[@dianarodriguez6112]

Thank you very much for your excellence at explaining this topic... I ve watched the whole playlist and it helped me a lot to understand game theory. Not often do i find a professor who explains as clearly as you. Keep it up

[@raichu56k]

this is so interesting, so excited for my game theory class this semester now

[@cyruskhamneipur6599]

I believe you've neglected to take into account the increased likelyhood of stitches for each player if they confess as snitches have a nearly 100% chance of recieving them. Great work, thanks for these videos.

[@Lrripper]

Oh it actually makes sense now. The reason why the rule exist is to counter this strategy

[@TheMadJestyr]

Thank you and I will continue to watch this series, it is very well done.  I have always wanted to know what game theory was and I appreciate your efforts.

[@rednails14]

You just helped me with something I've been trying to figure out all day, and I've got a midterm tomorrow. I can't thank you enough!!!!!!!

[@somebody539]

Thank you for Your Lectures ,its really amazing and Easy To understand !!

[@MissCleOh]

Thank you so much for this!! You're so much better than my lecturer!!!

[@tiaran83]

Mr. William Spaniel. This is fun! I never thought I would ever call math "fun" hehehe. I'm watching this playlist for a video competition. This was my idea choice and I convinced myself all these videos would do no good. I was wrong for sure! So much information, I am now confident to win! Thank you, also if I am asked about this I will know what to say! human minds are a wonder!

[@stephendelacruzone]

Neat idea! 👍🏼 Had me fooled with the first option though. 🙀😁

[@mkwarlock]

A lecture in university today covered some of these topics.. It was one of the most interesting lectures this year. Thank you for your videos, they are amazing. I am also planning to buy your book, because I'm planning to do a research project on this for that subject (Intelligent Information Systems).

[@mohsenbehzadkarimi4595]

Keep up the good work

[@kirillous]

Can you also solve it using expected value? Assuming chances of confession from other player is 50/50 E(quiet) = -6.5 and E(confess) = -4, so confessing for us is more beneficial

[@JD-jl4yy]

Humanity is and always has been a prisoner of the prisoner's dilemma. Humanity's greatest challenge for the future will be solving this dilemma.

[@Trantaloid]

And a victim of irrational actors. I understand the value of these concepts on an autistic black and white level but the reality of the prisoners dilemma is much more complicated, like what consequences besides more time will ratting the other out be? Like getting killed for being a rat. How could you even come up with a probability to use as a factor if it is almost certainly non zero.

[@uristrauss6106]

This series is great. A model for how to do a class on youtube.

[@lllapland]

amazing explanation

[@joeswanson4329]

Thank you so much!!

[@ulysses8910]

I think this could be applied in a real situation to make two criminals to confess

[@PunmasterSTP]

I'd say this video has some strict dominance in terms of quality of educational material on KZbin!

[@OliviaGrace1194]

You teach this better than my professor

[@avramprimack7373]

The choice depends on if there are other factors. If I threaten the other player before we are interrogated I might make other assumptions, and vice versa. If the penalty for confession is larger if they both confess than if only one confesses then I might make other choices.

[@julkkis666]

i find it kind of interesting that no-one here looks like they're commenting about having seen your newer videos 🤔 interseting that you have been making consistently this kind of content, ofcourse with some audio quality improvement etc :D

[@nobodynowhere9591]

Great course

[@RuthieOnTheMobile]

You are making my choice harder now. I have the choice of two courses. An older presentation in its final year that doesn't have game theory and its updated presentation that does.🤔

[@sallynall7228]

If player 1 assumes that player 2 will confess, then he should only confess if he is interested in minimising his individual jail time. If he assumes that player 2 will confess, and he keeps quiet, then there will be 12 months served in total, as opposed to 16 if they both act out of self interest. If player 1 is wrong in his assumption that player 2 will confess, and she actually keeps quiet, then they will each serve only one month. I understand and agree with the principle explained here, if there are two conditions stated beforehand: that each player is acting selfishly, and that this is a discreet event and actions performed during this event will have no bearing on future events. Unlike dispassionate probability, it is not reasonable to treat human interactions as discreet events.

[@immabesuperbig]

Sally Nall yeah he did say that the assumption is each player only cares about themselves

[@qwertzuioppel]

this assumes both players only care about themselves. if we assume they want to minimize total jail time, then confessing is strictly dominated instead.

[@thekingprajna]

Thanks a lot

[@zzhaier981]

Two ways to solve the dilemme: love each other; ability and willing to consider the big picture.

[@haggismcbaggis9485]

If you examine the grid from a utilitarian perspective or the greater outcome, the keep quiet camp results in lesser total punishment than confessing.

[@TheMadJestyr]

Maybe I am too philosophical about this and just don't know enough but this only takes into account individual greed. This assumes that each person only wants to do what is best for themselves and not able to predict the outcome of each thing. I personally do what is best for myself if and only if it doesn't also hurt the collective. I also would never pick a partner in any venture but specifically in a crime if I don't know that the other person feels the same.

[@gamesnikuya5474]

Thanks, Im a grade 7 student and science class. I watch these for additional education

[@mananaron8469]

So what would be the rational decision here? Is keeping quiet rational or irrational? And is startegy of keeping quiet strictly dominant? If not which startegy is strictly dominant?

[@javadeveloper9442]

Dear, I started my PhD journey, and my background is not in the game theory, yet it will be a good new chalenge. Will your videos and book assist me in understanding how to utilize game theory concsepts in cyber security or machine learning ..etc.

[@sorro9384]

we need a prisoner break dilemma !

[@nathanlin8297]

this is actually an explanation for the "dark forest' state in liu Cixin's remembrance of earth's past

[@goodlookingcorpse]

It's interesting that this game implies that criminals will claim never to rat, will actually rat, and will attempt to punish others who rat, all of which sounds like what happens in the real world.

[@sidddddddddddddd]

For player 1, if he confesses, he strictly dominates the Player 2 if Player 2 keeps quiet but if Player 2 also confesses, both of them get the same utility i.e. -8. Hence, this would make ‘Confess’ a weakly dominated strategy and not strictly dominated as opposed to what you said in 3:41. Or am I going wrong somewhere?

[@Supersonicboom7]

Very interesting, I guess this is where snitches get stiches came from. It's a result of understanding that the only way to beat the system that incentivises snitching is to mixup the incentives so that snitching carries a real consequence and is hence less attractive.

[@EzeBall1710]

This shit interesting as fuck bro😭😭

[@lassman8488]

SIGMA robber : let's Both shut , and plays the game inside

[@bitsbard]

Your content is truly compelling! For more of this, I'd recommend a book with akin subjects. "Game Theory and the Pursuit of Algorithmic Fairness" by Jack Frostwell

[@StarsTogether]

Exquisite work! If you’re engrossed in this, a related book should be your next read. "Game Theory and the Pursuit of Algorithmic Fairness" by Jack Frostwell

[@Starfan7]

if the prisoner's could convince the interrogators to give utility if either of them confess, then i calculated that equilibrium would be confessing 20%, is this right?

[@henrimessinghausen5185]

The one who confesses will be very very sorry after I get out of jail in 12 months....

[@ViennaRobert]

this might sound petty... but i have seen quite a few discussions break over why the guy who confesses would get off scott free. where it would make more sense if the guy who confessed gets the full sentence and the one who shuts up gets off free. it usually helps to add a simple sentence explaining why he would get off free :) or to add the other version.... then non dominant?

[@Gargantupimp]

The players that confess are now known as snitches to the criminal community and get shanked to death in the prison showers, they're both ok with this because they were only interested in minimizing their own sentences.

[@Starfan7]

Actually, there isn't a rational way to change it to allow for mixed strategy equilibrium, is there?

[@PixelPioneer176]

I'm loving the depth of this! If you feel the same, a similar book will not disappoint. "Game Theory and the Pursuit of Algorithmic Fairness" by Jack Frostwell

[@masskiller9206]

From personal experience, I completely and vehemently 100% disagree with the sensible outcome being to both confess. Do not commit crimes with people that will confess.

[@thechannelthatdoesnotexist]

the point is that you can't be sure if the other person will confess or not. you choose to confess out of fear not out of selfishness and the other person is thinking the exact same thing and there is a high chance that they will choose to confess because they can't trust you. they wouldn't want to risk 12 months in prison and so wouldn't you. you can only trust your close family member with whom you've spent your entire life otherwise you can't trust anyone else. you see selfishness is not evil and we as a species wouldn't have come this far if we weren't acting for our self preservation. selflessness doesn't exist and the only things you can call selfless are robots and machines.

[@NuncNuncNuncNunc]

Yeah, the real world has those pesky externalities like snitches get stitches that simple theory can ignore. A real world payout would be a function of jail time and street cred.

[@moraloverstance4093]

Let me be realistic here: The police could lie by saying the other prisoner has already confessed. So, you have to confess to avoid staying in prison for 12 months. Or, force you to confess by punishment and torture. In the end, no matter what you do, you both are going to be locked in prison for 8 months. Therefore, I believe it has nothing to do with “dilemma“ since the prisoners have no choice but to confess. Also, you said that each prisoner only cares for himself, they don’t trust each other. So naturally, they both have to confess. I don’t get why they call it a “DILEMMA”.

[@owensvideos]

Why does (confess, confess) = (-8, -8) and not (-12, -12)? Does this assume clemency equals -4?

[@BlademanZX]

+owensvideos Probably something like that; the one who kept quiet is getting punished for the crime and for withholding the truth, where as if they both confess, they're only being punished for the crime. Something along those lines.

[@kaloyantrayanov3559]

the best strategy here is to stay home :D

[@critical_always]

Virtue signalling is vile.

[@clintwestwood4545]

SNITCHES GET STITCHES!

[@UnderscoreZeroLP]

Anybody else learn this from The Selfish Gene by Richard Dawkins?

[@Rc-tb9uy]

You’re forcing what both will do. That one will confess and one won’t, in a real world, it makes sense for both to keep quiet, but that’s a bet if you have no idea. And in reality, a situation like this is totally unpredictable what one would do.

[@Rc-tb9uy]

It make sense for both to agree to 1 month. Let’s not act like they have thought about the probabilities of outcomes, and if they are, they would agree to 1 month. But then one could dick the other over.

[@TheOneAndOnlyKurtNobrain]

You sound alot like Maynard James Keenan of Tool.

[@chasewoood7363]

what does MOOC mean?

[@Gametheory101]

Massively open online course. It was a big buzz phrase three or four years ago that has since died out. #honestanswers

[@the_master_of_cramp]

Okay, seems like this model is not good then. We should bring in some probability of betraying one another in. Depending on the betrayal probability there will be a better average outcome for both.

[@kaloyantrayanov3559]

All viewers will have -8,-8 now..

[@kazisiddiqui6435]

This scenario doesn't reflect real life. Here, the game ends with the sentencing. In real life, the guy who confessed has to live with the social consequences of disloyalty. This maybe better represented by Prisoner's Dilemma as a game that is played sequentially, with past loyalty being a factor in future decisions.

[@mfbias4048]

I dont think you understand the point the point of the video

[@oO-es6xb]

tanemmirt

[@postwoman1802]

3:40

[@brandongibson7050]

This reminded me of Andrew and Tristan Tate's situation.

[@franklinohlin8224]

I would not last 5 minutes in this class

[@drwdzz]

Wait a minute Joe Biden! In the first video it was 5 years if they both confess. Come on man.

[@csacad2573]

Bro is talking at 1.25x speed, i need to play the video at 0.75x nevertheless its great

[@jaysonp9426]

This assumes people are rational

[@benjaminbeitz4023]

As of today this video is 11years old, ahhh those days when there were only two genders

[@ariana6318]

Did you just assume their genders?????

[@col.waltervonschonkopf69]

Snitches get stitches!