Game theory challenge: Can you predict human behavior? - Lucas Husted
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- Опубликовано: 4 июн 2024
- Solve this classic game theory challenge: given integers from 0 to 100, what would the whole number closest to ⅔ of the average of all numbers guessed be?
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Given a range of integers from 0 to 100, what would the whole number closest to 2/3 of the average of all numbers guessed be? For example, if the average of all guesses is 60, the correct guess will be 40. The game is played under conditions known to game theorists as “common knowledge:” every player has the same information- they also know that everyone else does too. Lucas Husted explains.
Lesson by Lucas Husted, directed by Anton Trofimov.
Animator's website: www.antontrofimov.com
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The results are in! With over 5,800 responses, the average guess was 8.96, so the correct guess for 2/3 of the average was 6. 169 people (3% of those who submitted answers) guessed the right answer. Well done, 3%ers! Thanks for playing, everyone! Keep an eye out for future game theory games.
Yes
@@timezone5259 my guess is 6
I'm gonna post it in the comment and you can't stop me
But when will you do Think like a coder episode 3?
my guess is 100
Anytime Ted-ED poses me a question starting with "Can you...", I already know the answer's no.
Me too 😂
😂😂😂
im her wondering : what do you mean by :"what the two thirds of the new average will be. "
This is called self-fulfilling prediction.
Can you comment?
Can you spell?
Can you think?
Can you talk?
Basically the scientific explanation of the "what if he knows that I know that he know that I know that he knows..." phenomenon...
And I enjoyed it ")
they know that we know that they know that we know...
@@neogery Monica Geller entered the chat.
I hate that. Cus then he know that I know
but I know that he knows
but he could not know but say he does
but I my know he knows that he does not know
I thought the same thing!!
Y did this help me understand the theory better than the video did?
They know we know they know we know
Joey Tribbiani dislikes this comment.
I was actually able to understand this
The messers, become the messees! 😎
Oi bishal katuwal?
Yeah, I know.
k level reasoning in daily life:
Rock paper scissors
Daily? The last time I played that was few years ago. Oh god, I need some friends
Yeah it's a super good example. You need to think ahead but ypu are scared that your opponent will also go ahead so you end up tying all the time lol
Get this guy to 1000 likes
In Rock Paper Scissors if you have a k level of zero you have a 1/3 chance of beating your opponent if they over think
@@FalseRadiation XD yes!
I'm operating at k level 0 at all times ✌️✌️
same haha
Says the k-level 10
Brilliant
It's the only way to operate
So "meta" of you.
K1 for me (I hope I got the logic of the video exactly)
had a stroke watching this
Ok.
What
HAHAHAHA
Also, if this is true, have a SLT check for symptoms of dysphagia ASAP! This could save your life. (A Lil information never hurt anyone!)
@Eric Lee 1/2 of all strokes are linked to dysphagia, which can be deadly if left untreated. A certified speech and language pathologist should run a screening test asap, to check if the patient is in danger or not.
Well, imagine me, not native english speaker, trying understand all that he just said. And even if was in portuguese I think I wouldn't understand totally. At least I tried lol...
What smell is this? Did someone burn something?
Oh, nevermind that's just my brain trying to comprehend this.
_😆😆😆_
I was like whaaatt is he talking about
😂😂😂same
Right, right, because you are so shocked and surprised at how much irrational people really are, I get ya.
Me to my brain:
Its okay brain you can take your time.
"everyone knows this"
Me: 👁️👄👁️
Lol
Lmao
🤣
Even if everyone knows this, it'll be the same since you'd know that they'll do it, and you can predict them easily.
This concept was explored in a game from the "Alice in Borderland" series. It was basically the survey, but if you guessed wrong, sulfuric acid would kill you. Fun!
yessss that was a great manga
It is also a live action show on Netflix.
It reminded me of that as well. Chishiya is just too good 💀
"In real world, people aren't perfectly ration or doesn't expect others to be perfectly rational"
Well hot daaamn, story of my life - said almost everyone
True and so that i avoid people ....☺
*rational
The k-level reasoning thing reminds me of a manga named 'Liar Game' that's so satisfying to read. The main characters are geniuses playing psychological game against each other, using this multi-level way of thinking ahead.
It's just plain awesome.
Hiền Anh Trần yeah, it is very related. I did a phd in game theory (behavioural science) and illustrated these games to my colleagues (postdoc and professors in game theory) at some point and they were also intrigued by them. At some point we considered doing an experimental variation based on the stationary roulette game based on the manga. 🙂
thank you for the sauce!
read classroom of the elite
That's worth re-reading again! In fact there's a drama based on it. Not sure if it's still around though...
everyone: it's should be 0
me: what was 2/3 of hundred again?
66666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666
If i counted correctly that's almoust 2/3 of 10^883
@@mcventi4859 i believe it's time for you to learn a new symbol.
When it comes to human behavior, it depends on how well you know their habits and ways of thinking. Due to how complex humans can think and how smart we can be, there would be multiple results on how we could act and it would depend on how well we know people and humans in general.
Yeah it’s much easier to tel when you know the person you are trying to predict with strangers it’s much harder
When you say 21 out loud ironically to yourself and then you’re right
I said 20 ;-;
I said 22 haha
K Level infinity
I said 15 so I am correct about real world conditions ;)
I also said 21 we all know each other too well
Lol we were just talking about this in my microeconomics class
Uct
Which topic?
What's interesting is that if you convince everyone to choose 0, they all win but if one of them chooses something else nobody wins.
If you explain that to every participant they could all choose 0 because otherwise they lose.
But there will be at least one troll that wants to screw everyones winning chance...
yeah that's literally what i thought . you'd have a couple of trolls choosing 100 , and a couple of rational thinkers understanding that there would be trolls , so they increase their bet them selves . and the cycle repeats , that's why the result was an off 6
No, everyone who chooses 0 wins because they are closer to the answer.
@@inakiloriente the rules didn't say that you win by being the closest to the answer
@@fraidei2094
Implicitly, they do. They said that if everyone guessed 100, the winner would select 67 (or maybe 66). Either way, that's not actually 2/3, but just close to it. Maybe they meant that the winning guess is 2/3 of the average but rounded to the nearest integer. Even if so, with a large group, if there are fewer than 1% trolls, everyone who picks 0 wins.
@@timthielke3541 The problem is that out of 1000 people in the internet you have round about 200 trolls, 300 morons, and another 300 idiots. With this being a filtered bubble, you can assume that on Ted-Ed these numbers are a lot smaller, but they're still there, and it's more than 1% - even on this channel.
"Want more game theory?"
.
.
Uhmm...I think my brain had enough for today.
100 likes with no reply??? I'll help you break out of this awkward situation :)
Btw I AM THE 100TH PERSON TO LIKE THE COMMENT NOT ANYONE ELSE
I'm K negative.. because there is category group of people who didn't understand the question itself...?🤔...includes myself🙄
LOL
I am in that group too, maybe because I didn't see the original wording or maybe there was a video explaining the question that I did not see.
well like its simply trying to guess what everyone thinks like at k0 no one thinks so u go with a random number but at k1 u assume there are k0 ppl and try to guess a number now u assume there are k1 ppl its basically u having a certain thought process and answering based upon if everyone had the thought process . And a tip if u are trying to understand things easily try to like explain it to urself out loud as if u are explaining it to someone else if u read this thank you for taking time to read this.
The question is really 3 steps:
1st: people guessed a number between 1-100
2nd: what do you think is the average number guessed for all numbers recorded?
3rd: The real question. Now that you have that average number in mind, what whole number is 2/3 of it?
So if you think the average was 60, then your answer is 2/3 of 60 which is 40.
I know your comment is old but I hope it helped!
star trillion I’m confuse how people would be able to guess the right answer
If I were a math teacher, they wouldn’t let me teach Game Theory bc I would end every class with « BuT tHaTs JuSt A tHeOrY »
A gAMe tHeoRY
1 is also a Nash equilibrium, because they phrased it as the "closest integer to 2/3 the average guess", so if everyone guesses 1, everyone is right, (since the nearest integer to 2/3 is 1) and more than 2/3 of participants would need to guess 0 (with the remaining guessing one), in order to shift the answer to 0. So, while 0 is a Nash equilibrium, so is 1.
Thanks! Happy to see I am not the only one who is “that guy” ❤
that k level thing sounded familiar, and then I realized that was how I played club penguin card jitsu
same
sameeeeee!!!! i get so stoked whenever i have a 6 game winning streak lol
@Abhinandan Katoch Back when Club Penguin was still around, the idea was that you had a trio of basic cards. Water, fire, and snow. Fire beats snow, snow beats water, and water beats fire. Cards are numbered 2-12 and if you guess the same element, the one with higher numbers beats the other, and if they are still tied, the round is null.
Each card also has a colour, and so you win by either having three cards of the same element in all three different colours or three cards of different elements of three different colours. You can see what your opponent's colours have been, and have a record of your own.
Ergo, you are able to guess that the other player will be more likely to choose cards that help them win the game and get to that diversity of cards, but the other player knows this much of you just as much and also knows that you would prefer to play cards that help you win in the same way, and you know that they know, they know that you know that they know, and so on. It was a brilliant game.
For the “second round” of the 2/3 game, I’m expecting at least half of the people to remember “0 is the best answer” and pick zero, and half to pick random numbers, pick 100 to be trolls, still pick 50 because the math is confusing, or pick 60 because the math is confusing. I pick 33.
If we're all smart and we know we're all smart, then the question essentially is...
What is the value of x if 2/3 of x is also x?
Now I'm so mad I didn't get this post in my recommendation.
0
@@isieg575 yes, exactly, as the video said.
@@whynot9579 I'm not smart enough to explain with the inclusion of dummies as they can not be predicted without statistics.
@@whynot9579 If everyone playing is a perfect logician and also knows that every other player is, then the reasoning is as follows: There will be some average x, since everyone playing knows this and also knows everyone else does etc. everyone will guess 2x/3 so the average will be 2x/3. But we defined x as the average so we have x = 2x/3. The only solution to this equation is x=0.
Of course in practice the average is almost never 0 and there are reasons to guess something other than 0. One is if you're not smart enough to figure out the game, another is if you think other players aren't smart enough to figure out the game, or you might think other players think that other players aren't smart enough, etc. making this difficult to win with any real consistency.
@Eric Lee move the terms to one side then factor then divide. x = 2x/3 -> x - 2x/3 = 0 -> x(1 - 2/3) = 0 -> x=0.
You can also kinda "guess" the answer by noticing any other number would change when multiplied by 2/3.
BUT THAT'S JUST A THEORY
a game theory!
a game theory theory!!!
@@jellyfishjelly1941 Thanks for watching
Omg this joke fits so well here
A FILM THEORY!
proud to say that after a few months and a rewatch i understand what he’s talking about
Growth is a process - let’s keep at it!
Everyone guessing 21 cuz of the meme and actually getting it: *surprised Pikachu face*
2/3 of 21 ain't 21 so everyone lost🤔
@@vaibhavpandey7202 wha?
Which meme?
What there was a meme?
@@ritulakhani8535 I guess its 11 + 9 = 21 meme
Trust the actions, not what you hear from others, not what you believe...
Not every one thinks that way. So you thinking that way really just makes you a follower and not a leader. Unless now that you said that everyone is going to start thinking that way...
@@saphired02 well no. You don't even seem to understand the meaning of that sentence. Human can use lying words but not lying actions. Their actions reflect who they are because words and thinking can be deceived.
@@KAIKIN Even actions can be decieving. To truly get the best outcome, you have to utilize all of them equally, and even then, not every situation is the same.
To rely only on one sense is setting yourself up for failure.
@@skrrtskrrt2410 well yes actors are some counter examples. What i meant was IRL actions are more trust able than words. Just look at the politicians.
@@KAIKIN Oh you sweet summer child. Ever heard of ulterior motives?
This is alice in the borderland
"The weather today is partly suspicious with chances of betrayal."
- Chuck Palanhuik, Diary: a Novel
King of Diamonds game!!! Was so not expecting to find this. Now I understand Chishiya's reasoning :D
K-1: What do you think I'm thinking?
K-O: That I'm a "Knock-Off"?
*At the end of this video,I'm still confused*
3:57 Rare footage of Manchester United's only goal in 2019
Thank you so much for this game theory video! This stuff is super fascinating and it's hard to find well-produced videos on it like this
Ah, the old game of "they know that we know that they know but they don't know that we know that. Or...do they?
i had a stroke reading that
some people know but some don't and only some know that some know and some don't.............................................
I would still go for 0 even if its unreal ^^
I always thought of people's decision making being based on their 'level of thinking', which was dependent on what level they thought the opponent was on, and thinking one level higher than that. Like how chess masters think ahead of their opponents, and how in death note L and Light used multiple layers of reasoning.
Today I learned it actually has a name, and is called k-level of reasoning, wow.
Yeah constantly trying to outsmart in death note
Very fascinating, looking forward to the results.
2:07 *My dog, silently watching me and my sis fighting over the TV's remote*
My cat : 👁️👄👁️
"1" would be a more robust choice.
2/3 of 1 is .66 which rounds to 1.
1 is closer to higher numbers than 0, so it would tolerate more change from people guessing randomly (since their average would be closer than if "0" was picked).
Basically 1 is also a correct choice, so I don't see a nash equilibrium here. And if few people were to answer randomly, 1 would yield a more robust average, being more tolerant to changes while still granting a win if everyone acted logically.
Dude nice math! 👍
If you choose .66, the 2/3 game still applies, so it'll forever get closer to 0, between 0 and 1 you can find an infinite quantity of decimals... It'll always get closer to 0...
@@Eshkirbel1 but I chose 1, not .66
@@Eshkirbel1 you can't choose .66, as you have to guess "the whole number closest to 2/3 of the average of all guesses"
I’m in love with this channel and their topics❤️ Thankyou for such informative insights💯 Grateful!
This was a surprisingly difficult question to answer. I’m very excited to see the results!
I want to learn to predict my friend's and enemy's next line
Was this your plan all along, *JOJO* !?
*Impossible!?!?*
YOUR NEXT LINE GONNA BEEEE.......
Niceeeeeeeeee
Finally, a TED-Ed challenge I knew how to solve before they explained it! Just learned this a few weeks ago in my evolutionary game theory course.
Sounds a bit like Princess Bride’s The Battle of Wits.
Iocane powder
K∞=poison both glasses
I thought of that too :)
I understood that reference
Lolol
I am a math and economics student and this video is one that made me feel proud about my academic formation.
What you guessed?
2:01 That summarizes all my ranked matches in LoL
this is also called the keynesian beauty contest! one of my favorite concepts in math
i guessed 0 after like 40 seconds of thinking, someone needs to get me off my high horse
You guessed wrong then. The point is to get the answer that reflects what other people will have chosen, not find the nash equilibrium. No horse needed.
*"Shall we play a game?"*
*- Jigsaw*
*I summon Slifer the Sky Dragon!*
-Yami Yugi / Yugi Muto
Short, sweet and got me a good understanding and filled with good detail and good material.
video: **has "theory" in the title**
everyone: _bUt tHaT'S JuST a tHEory_
“Objective facts are Nash equilibrium points in the contest of competing wills.”
0- as I feel like once everyone’s been told the most logical knowing that everyone else was told it they should all go there?
They said don't post your answer here, there's a link in their top comment to a website they want people to give their guesses at :)
I'm part of the people believing not everyone is rational. Theorically, you're right but it's the internet and people are gonna troll and post other numbers. It's almost impossible to tell an entire community to do one thing if they have the opportunity to change the stakes
0 is the most logical if everyone thinks the same, but take me for example, I believe there will be people that won't choose 0, so I'll choose something bigger than 0, if there're many people like me, even knowing the logical answer, we won't answer 0. But what I can guess is that since more people know the most logical answer is 0, the new result will be closer to 0.
Just btw, to this question, the answer at the highest K level also, given that the average is to be a whole numbered value and the numbers whose average is taken are also whole numbers, would not reach 0. It would be 1. This is because at the last assumption, 2/3rds of 1 is 0.67 (but only if we allow non-integer type values, which are not allowed). This results in the 0.67 to be converted back to 1 (as 1 is closer to 0.67 than 0), n then this process is repeated infinite no. of times, each time the no. being 1 n not 0. Therefore, the correct answer (assuming everyone is K12 lvl intelligent), should be 1 n not 0.
I love Ted-ed! ! Waiting for your upload!! Thanks for the video!😍😍
A: “I knew you were gonna do that so i did this”
B: “I knew you were gonna do that so i did this”
A: “I knew you were gonna do that too so i did this”
Hey TED just a reminder, your subscribers are not that smart.......
BTW thanks for sharing Knowledge as usual.... You are the BEST.....
>Tfw you guessed 22
>Tfw you forgot about the average
Well explained. Well animated. Perfect.
I would like to point out something that I think ted forgot.
Since the question is to select an INTEGER from 0-100 then once you reach to 1 and then take 2/3 of that, after rounding it you get 1. Thus you will never get to 0 on any k level.
it confuses me with that 67
That's exactly what I thought.
It would have been interesting to see the graph of the guesses.
If Rock Paper Scissors counts, I predict everyone’s moves while playing that game
I personally think it counts
this is by far the most interesting channel to learn things
21, a meme, was the right number... wow. Ted Ed is a legend
Who’s here after watching Alice in Borderland? 😂😂
Like always, awesome video... so... what were the challenges again?
Also i love all your videos and I've subscribed your channel too
Step 1: Confirm you have green eyes
Step 2: Ask Ted-Ed to leave
This is funny and unfunny at the same time
Holly cow! I thought everyone would say 0! This video just blew my mind. I'll now expect other people to be dimmer then I expected before. This also gives insight about how many steps ahead people usually think, which is nice to know.
It would be a true leap of faith to think every single person in a room would choose the exact same answer while they simultaneously trust everyone else to also choose the same answer based on the same reasoning.
I wouldn’t bet my cat on it.
What a beautiful video to depress people like myself who can’t even comprehend 80% of the video. Nicely done Ted-Ed good job 👏
kinda hard to wrap my mind around but im amazed at the possibilities
"Hello Internet, and welcome to Game Theory!"
No one:
Joepsh Joestar:
Niceeeeeeeeee
So sometimes it’s beneficial to think less. I am gonna be SOOOOO good at that!
i love watching these videos
Is the dialogue from The Sims? 😂
I went straight to zero.. That means I was expecting others to play in the most logical way.. which turn out to be not common.
ay, same (turns out it's more common than you think)
that's in fact a missing logic level from yourself . you should guess that there would be trolls increasing the value on purpose and other thinkers guessing that trolls would do that , there for they would also increase their bet , and so one .
I chose 44 because middle ground somehow
This video is that what I needed
👍Thumbs up. Enjojed this
But remember! It´s just a theory, a GAME theory!
My guess was 22, I'm so proud of myself.
Mind blowing !
@0:24 I think the use of past tense ("...of all numbers guessed") here obscures what is being said. When the game is described as guessing 2/3 of the average number "guessed" that makes it seem like another group of participants have already picked numbers from 1 to 100, and the current participants are trying to guess 2/3 of that. It is better to say that the goal is to pick a number that is 2/3 of what the average guesses *will be*.
So, when someone says they're on a different level, this is what they mean.
but hey that's just a theory
*A G A M E T H E O R Y*
Aaaaand cut!
*A G A M E T H E O R Y T H E O R Y*
Thanks! This should help me with the Ted-Ed riddles
Most people stop at 1 or 2 k-levels, so sharing the information will add an additional 1-2 k-levels such that the total becomes 3-4 k-levels. Thus making the mean guess ~(⅔)^4, and the answer to the game ~(⅔)^5 = 13.1
Well if everybody is logical then zero if their participants all know, but, we all like being a little different so; i'll say 4
If everything explained went above your head we should be friends 😂✌️
Rakesh Raveendra Yaaaay 😂
This voice is so good & does a good job
I paused the video at the beginning to make my guess: 13.
I figured the other people's answers would be a combination of people guessing zero or one, people guessing two-thirds of the average of people guessing at random, the people who actually are guessing at random, and a few people misunderstanding the question and just guessing two thirds of the total.
I always watch these videos thinking I will understand them... Silly me 🙃
When you are from Denmark and you hear them say politiken
Nej nej Nej
I'm Dutch but even I crinched
Ej den er gal
Then how do you say it?
@@anteater9408Difficult to explain over text, try searching online
@@ajani-lamar-_-3712 I googled it and heard "politeekuhn"
I love how I click on these every time thinking the videos will be simple
I think the difference between K level 2 and any K level larger than 2 is a lot smaller than the difference between K level 2 and K level 1.
It's like in the classic scenario when two people have to drink a drink one of which is poisoned and they have to figure out whether or not the other person switched the drinks and if so how many times (or "did they switch the drinks... or is that just what they want me to think... or is THAT just what they want me to think..."). To get to K level 1, you just have to ask the first question. To get to any K level larger than 1, you just have to ask the second question.
So K-level is basically "I know that you know that I know that you know that I know that you know that I will do X."
All this math have me confuse 😂
Me too
Hello fellow k-0s
I’d recognize that the answer shrinks as you do additional loops and guess the asymptotic limit: 0. What k-level is that?
Damn,does it mean I’m at K-level 12,since I thought that 0 is the best option for everyone to choose and picked it myself?!Some geniuses out there
Dima Maksimov i hope this is ironic.
Mathieu P. Corbeil it is,buddy;)