Prisoners' dilemma and Nash equilibrium | Microeconomics | Khan Academy
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- Опубликовано: 1 окт 2024
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Why two not-so-loyal criminals would want to snitch each other out
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Evolution of a Mathematicians career :
Undergraduate => Graduate => Assistant Professor => Associate Professor => Professor => Prison Warden
> Pizza delivery
I want to see my lawyer first.
Nice try, FBI, but I'm still not confessing.
That's funny. Game theory for the cromagnon jock.
Plead tge fith upon intro
Lmao 🤣🤣🤣
For some reason, i can never sit through the lecture of my professors, i'd either fall asleep or get bored with their analogy and start tapping on my phone but surprisingly I would sit through your videos and just keep replaying it if i dont understand it. Anybody else going through the same thing i am ? I also would come to your videos before going to any of my professors just because you are much more easier to understand.
You could drop $150k on an education that you could get on RUclips, then buy a sheep skin and transcript off the darkweb.
I'm sure if your professor would have a smartboard, a nice voice, and an easy example you would go to his lectures. We, like people, have changed over the past 20 years or so. Since multimedia became mainstream we changed our attention span and our expectations for entertainment. There have been numerous studies on our attention span. One showed that, because of cell phones (social media scrolling), our attention span has significantly decreased, which means we 'can' only comprehend something for a short time before getting bored and 'scrolling away'. Another thing is, we get bored by plain text, plain speech, etc. One of many studies showed that the same post (same text, same information) gets less attention (fewer likes and comments) on Facebook if it's only in plain text instead of a text and picture (without taking into account how related the picture is). I see asynchronous learning (videos) as the future of learning because you have a multimedia format (speech + pictures, graphics, videos) with enriches the experience (most of us are visual types, hence it helps us to understand something when it's already visualized) and helps remembering stuff (there's been a psychology experiment I think in the '80s where they tested short-term memorization of words by just reading them and a technique that uses non-related visuals, i.e. for each word you look at an object in your surrounding), and you also have the options to replay the video or pause it as you like, in that way dictating your own learning tempo.
@@matik0701 That experiment in the '80s reminds me of learning a new language using Rosetta Stone. They say the word and show the picture. Brilliant!
This is one reason people sometimes confess to crimes even when they are innocent.
"This is one reason *fools* sometimes confess to crimes even when they are innocent."
FTFY.
With the american judicial system of juries giving out a verdict, can't say if they are actually fools.
@@akshatgupta8523 exactly, well said.
In some countries admitting a traffic offence is cheaper and time saving than fighting/ reasoning it. Wonder if it falls here
"Capturing the Friedmans"
I'm Al and I'm denying, hopefully Bill will do the same
well, I'm Bill and I have one bad news for you
@@kimyongun5471 o your kim
I'm baffled by the fact that Sal hasn't won the Nobel Prize yet.
You are easily baffled.
he has not, but the person who invented this method, John Nash, won the nobel prize :)
@@mohammadomar6680 thank you for explaining this, man, I was baffled too
@@NibsNiven Lmao. Give him a break dude he must have been cursed with bad professors and sources.
I am honestly fascinated by that perfectly written 'g' in the word 'drug'
I'm more fascinated by the invisible 'l' and 'i' in "Equilibrium".
It's a nice g
Hows the last 6 years been?
Bill Deny the Prisoner Guy
HAHAHAHAHA
Thank you so much omg. You saved me. Game theory is driving me nuts.
I'm really impressed. It's a truly interesting theory. I have seen the "A beautiful mind" and i was stunned by this incredible man (Nash). I appreciate video's creator helping me understand Nash Equilibrium.
RIP John Forbes Nash
Darn that spelling mistake. "Equibrium."
What about the added idea that the guy serving 1 year will probably get shanked and die for dropping a dime on his buddy?
Benjamin Shade
They're not buddies though. They've never met each other.
Benjamin Shade maybe they wore a mask while robbing the place
Sal does state outside interest is elimanated....nonlinear terms must be added in a subtle way. 😁
Its a shank or get shanked world out there. Shank the shanker to not get shanked. Dont shank the shanker, get shanked. Before yk it there will be piles of shanked bodies.
The explaining is wonderful and is easy to understand
Funny thing no prisoner considered a possibility that the offer was a lie...
We spent one class on this ... some 36 years ago. I have always been fascinated by this but never found the time to read further. A few years back that prof even passed away. Now staying home, I will learn this. Thank you Wuhan lol
Both deny is the state of " Pareto Optimality".
Why do you frequently repeat your words right after saying them?
3 years in prison with a reputation as a snitch is greater than 10 years in prison as somebody who got snitched on.
well you ain't a snitch for snitching on a snitch
But hey, that's just a theory... A Game Theory. Thanks for watching.
cleanseroftheworld hahaha
Man this guy has been helping me from Y1 of my comp sci course right to the very end
being a good DA is being a good hustler.
People dislike school but likes RUclips. How fascinating.
But the prisoners don't have the assurance that the police isn't lying right? Because if one of them confesses then the police may just jail both of them for 10 years because they now have proof
There's no need to repeat things as you write them. There's no need... to repeat things.... as you write them...
Is there an echo in here?
i searched long and hard for this comment
He got it wrong... if you confess you don't get one year in prison you get one year to live
hello people from ECO100, good luck with exams tomorrow :D
That's why we should make a universal rule. "DON'T SNITCH." There is never a reason to snitch. Snitches get stitches or end up in ditches.
They also frequently get screwed by the prosecutor.
BTW there is almost always a reason to "snitch". Crooks get away with crime because of spineless people. I "snitch" on people all the time and always will, because I care about more than myself.
this is why I snitch
Awesome dilemma but confessing to an armed robbery that doesn't exactly look too good once you're out. Well, neither does doing 10 years for drug charges lol
Are there any universal techniques to detect these in games?
I guess they will be quite obvious alot of the times, even moreso when you're good at the game, but it's hard to be good at a game still in developement..
I'm going to say the answer is probably no, and that I just need to get together some minds and do a huge load of testing..
And if they're problematic in the sense that they reduce the amount of viable decisions into a linear period of decision making, fixing them would perhaps be even harder..
While win win situation is not for everyone, we shall check further on John Nash and what is he trying to equilibrate.
Dear Sir Kahn,
I worship you, I really do, and I never thought I‘d see you giving a flawed explanation but today is the day. :-(
The way you explain it, it‘s mixing up the concept of „dominant strategies“ and „Nash equilibria“, which might be very confusing to students. In this special case of the prisoners dilemma, the state „confess/confess“ is both: an overlapping of the two dominant strategies „confess“ AND a Nash equilibrium (because the overlap of dominant strategies is ALWAYS also a Nash equilibrium), BUT a Nash equilibrium can perfectly exist without dominant strategies being around. They way you explain and derive it in the beginning, it seems that „confess/confess“ is a Nash equilibrium because it’s the overlap of the two dominant strategies „confess“, but the real reason why „confess/confess“ is a Nash equilibrium, the very core concept of the Nash equilibrium, is only what you start to explain at around 7:50.
So to every student who reads this: Don’t confuse these two concepts!
Greetings from a former RWTH Aachen Tutor.
Everytime you immediately repeat a phrase or word (and you do this A LOT), I lose focus because of how annoying it is.
+Ashkan Kiani That is also driving me crazy
good thing this video is free and you aren't being forced to use it.
barley 1 true, I guess I could be more constructive with my criticism :)
I too, was trying to provide feedback, but framed it poorly.
I find the opposite. Nothing get's into my head unless it's repeated multiple times.
thank you so much, the global equilibrium vs nash equilibrium helped SOO much. idk why anyone would EVER leave out the global equilibrium concept when explaining this. especially when nash equilibriums take into account unilateral incentive. THANK YOU!
Imagine being innocent and being convicted because some convict decided to lie about you so they can get a reduced sentence.
If they both confess ...it means they have a dominant strategy...
After having failed to get my head around this theory watching on Crash couse and Scihow, Sal came to my mind and it just paid off as always.
Sal is a true gem.
Thats why Going alone is the best.
One of the best videos on youtube. The explanation was very nice and clear. ❤️
As they say in the streets, snitches get stitches, and homies don't rat out homies. Prisoner's Dilemma doesn't work when there is loyalty amongst the thieves.
Well, what about the state classification of “snitch” where it doesn’t matter how many years you’ll be in prison because you’ll be dead.
Interesting concept though
😂😂☝️
I think I worded this wrong, but I’m just saying that the factor of snitching and repercussions aren’t included.
Good explanation. Only thing I'd say is that the risk of not confessing in this case is so much greater (8 more years in prison) and reward of not confessing (just 1 year less in prison) make it a no brainer to confess. If the reward for both not confessing was greater (say 5 less years of prison) then it would be more tempting to take the risk and not confess.
But the point of the video is to explain how the game theory works...which he successfully does
"a no brainer to confess"
Nonsense. It is always better not to confess.
I have introduced several thousands students to this theory and through social action prepared them for real life. As you can imagine in short run dishonest win, in long run honest ones. In fact 85% explain moral capital and firms and countries who play fair are winners. So God does control output, money is pure reflection of moral, intellectual, and social economy.
11th you 22nd, so 2nd 1 11th 11aw3 the 26th sq2q12 Q10 w32
"A beautiful mind" brought me here
can you fast forward the time it takes ou o type or type beforehand?
Al got red handed selling drugs, hahahaha
Double it and give it to do next person
It looks so easy when you explain it, but when I try to do it on my own, my mind goes blank haha
You also got to consider the after effects of your decision. If you rat on the other guy, he can be pis*ed off and get his gang to come after you...something not always considered in the game theory
In that case you have to change the payoff matrix, then in the case 2) if confess, other doesn't. You: 1 year + bullet, other 10 years. Same for the case 3)
This video could've been done in 1 minute
no
The short ones. So while u were waiting, on school and profession, gotta get a job u know, I got married to a wealthy man, upper class or low class , middle class. Ok, thanks for endorsing... Me, basically for sanity check.
Confessing to a crime you did not commit is perjury and thus is itself a crime. Conspiracy to commit a crime this is also a crime and therefore the prosecution should also be charged. The immunity of enforcing agents needs revisiting. If a judge decides a case that is later overturned the judge is thus incompetent and unfit for duty. This scenario is too unrealistic as there is no 100% certainty that the word of a confessing felon automatically proves anything against someone else, especially when (s)he has incentive to do so. Even non-criminalized people lie on the stand or misinterpret a situation so to believe absolutely based on confession is implausible.The only court system this works in is Japan's.
ive either thought about this equilibrium too much... or i was accidentally thrown into a parallel universe where everyone and everything part takes in a weird, oddly saddistic thought experiment with no end 😬 i suppose it is possible that the nash equilibrium itself, as a topic, causes symptoms of the disease suffered by dr nash himself.
What’s an economics application?
And I note that the penalty for risking the unknown and being wrong is severe in the example. That would likely be the case in investment and economics. Stock market investors hedge their stock investments to assure themes of “some” modest profits with greater certainty of success as opposed to taking bigger risks into unknown investments.
What if neither of them actually commited the crime though, but both confessed because they wanted to try and get a lighter prison sentence? Wouldn't that mean that those who were actually responsible for the robbery get off scot-free?
That's what the justice system wants. Somebody behind bars means your making money. They don't care who is serving the time for a crime as long as someone is.
They'd need more proof then a confession though. To really make the case though, the confessor has to say or show something that proves either he was in the case or both were in the robbery. Simply confessing isn't really enough to charge someone else
what if one of them was wrongfully accused and then DENY our of clear consciousness...so he will still have to spend 10 yrs behind bars....where as the guilty one will spend 1 .....or they never taught of making an equilibrium for this case..BULLSHIT!!!
two words: Ceteris paribus
This is the concept of most mathematical theories.
So once u explain with some cross cultural comparisons that the person thinks certain way and this is why they did not make it, accomplishments are accomplishments if u Patent one thought, or Newton's three laws. So he had three laws to Patent. The rest of us work hard to come up with one.
But practically in the real world, both criminals will deny and get to trial where both gets found guilty and both gets 10 years. What's the term for that?
While we don't know who we speak to or make acquaintances to, in America we arr now playing Einstein's bees. Just go around and hit people on the head.
Now education is truly free thanks to Khan Academy
GUYS WHAT DO I DO. i confessed and my partner got 10 years, he comes out in a few months.
Basically while a talented person sits and waits for his turn to come one million untalented people are still breathing, which really meant things were worse than we thought of so for ur own safety we can't take u anywhere
If they arrest too many tall people then lawyer can argue on heights and eventually release them all to become basketball players. Well, what about us?
It's about risk. Ratting out the other guy limits your risk from 5x to just 1.5x. It's a very good tradeoff given the potential risk.
So let's say someone ended up stealing. So on papers steal is 2 years unless ur lawyer reduces the sentence. When do u dismiss it?
*This is why mobsters use the same lawyer! NEVER TALK TO THE POLICE*
if they were both backbenchers they both deny as we never confess if other is only included in and i am not .🤣
Now what? Now, the so called prisoner knows ur face and follows u everywhere to harm u.
Serves a year, walkout free and clear, gets shanked at celebration of freedom ...
Your insights are extraordinary; just like a book that was deep in its exploration. "Game Theory and the Pursuit of Algorithmic Fairness" by Jack Frostwell
Thank you for doing this. Hopefully I'll pass my midterm now
There is a fallacy here, stemming from incomplete accounting of the payoff. Confession would also have cost, outside of what the police is offering, either in disadvantages to the prisoner in jail and outside, after release. Disadvantages range from threat to life to reduced opportunities. If you were to artificially valuate the disadvantages, say by forcing them to equate to just one incremental year of jail, then the dilemma has very different values in the payoff matrix, and deny becomes the only viable outcome.
Correct. This dilemma, like a lot of simplistic economics theory, is based on flawed assumptions. Too bad a lot of people buy into Nash's theories without thinking for themselves.
BTW not many people are aware that Nash himself stated repeatedly that his theories as people applied them were worthless. He came to regret ever publishing them.
@Knobcore "actually they're accurate"
@Knobcore "the method is [accurate]. the problem is it's always unstable"
@Knobcore Could you provide an example where the solution to a Nash formula is a complex number?
@Knobcore Judging by your gibberish reply I'm going to assume you have no idea what a complex number is. Sadly, your gibberish would probably qualify you as an ivory tower economist somewhere, filling young students heads with your nonsense.
This is off topic but I wonder if queuing (standing in line), where the serving time is proportional to (say) numbers of checkout items, could be treated by economic analysis in some way. While "first come first served" is fair (and upholds trust etc) there is the collective waiting time of for the people behind first place. People can switch in pairs, you see. So how could the line move to towards an 'optimal' arrangement under this type of approach?
Harvard and Stanford graduates get in trouble. Haha, just joking.
Pls share what if there are more parties how this concepts works.
Take a look at the Oligopolies, Duopolies, Collusion, and Cartels video.
One year isn’t enticing enough how about 3 months for snitching instead?
Both individuals, acting as rational decision-makers, opt for the less risky choice of confessing, given that the risk associated with denial is greater for both of them. In other words, they both select the three-year option due to its lower risk.
I understand this in the way of explaining Nash equilibrium, but from a law enforcement perspective how does choosing the "optimal" outcome from the prisoners' perspective (both confess) accomplish justice if the prosecutor was, in fact, wrong about his assumption in the first place about the other crime in question? He would have just gotten 2 men to confess to another crime they weren't guilty of and the real criminals get off scot-free. I guess it's proving that the Nash equilibrium actually pans out further than calculated? It certainly isn't good law enforcement, in fact, in many ways they've actually made things worse - justice was perverted in the case of 4 people (2 got away with it completely, 1 got a reduced sentence for lying, and 1 got an increased sentence for telling the truth!).
I think it would be good to present a caveat to this illustration in advance!
Another way to frame it ( per player)
best & worse scenarios when confessing is 1 and 3 years, respectively.
best & worse case scenarios when denying is 2 and 10 years, respectively.
thought this is a bit familiar and realized how watching Running Man for all those years helps me understand this more quickly. lol their loyalty test episodes are somehow like this 🤣
The globally optimal scenario would be: Deny, never show up in court for the drug charge and tell the police they have to prove beyond a reasonable doubt that he did indeed take part in an armed robbery.....split town and get 0 years....duh
Thank you for explaining this.
I loved it.
can it be the case that, Al actually did not commit the armed robbery and he denies? But he gets sentenced to 10 years given Bill actually committed the armed robbery and he confesses? In scenario would not fair though.
This one theory is at core of countries stockpiling nuclear weapon
is there a 5. option ? you confess and the other blames you on top of that.
I don't understand the fourth possibility. Why should both confessing mean a stiffer punishment than the original?
Somewhere in the world, before making their decisions... Bill and Al are watching this Khan Academy video.
I need antidepressants
Khan vict music... You Kahn do it!!! im here for that prisoner dilemma 23 32 10101 aint nothing but a G thing
Τaking into account one denies , the other would prefer to confess so 2-2 isn't the Nash Equibrium
Barack?
Finally it clicked 🙏 khan academy never disappoints
Senario V: Al confesses gets one year; Bill denies, beats the charge; gets two years. Al doesn't live out the year.
This video feels like Nash theory of law not economics
Im in love with your voice haha, you helped me so much during my bio exames
Nash has just died :'(
From the selfish point of view, from the altruistic point of view then 2/2 is the stable state...
Does this break down if for example the equilibrium state is 6 years instead of 3?