Game theory challenge: Can you predict human behavior? – Lucas Husted


A few months ago we posed a challenge
to our community. We asked everyone: given a range of
integers from 0 to 100, guess the whole number closest to 2/3
of the average of all numbers guessed. So if the average of all guesses is 60,
the correct guess will be 40. What number do you think was the
correct guess at 2/3 of the average? Let’s see if we can try and reason
our way to the answer. This game is played under conditions known
to game theorists as common knowledge. Not only does every player have
the same information — they also know that everyone else does, and that everyone else knows that
everyone else does, and so on, infinitely. Now, the highest possible average would
occur if every person guessed 100. In that case, 2/3 of the average
would be 66.66. Since everyone can figure this out, it wouldn’t make sense to guess
anything higher than 67. If everyone playing comes to
this same conclusion, no one will guess higher than 67. Now 67 is the new highest
possible average, so no reasonable guess should be
higher than ⅔ of that, which is 44. This logic can be extended further
and further. With each step, the highest possible
logical answer keeps getting smaller. So it would seem sensible to guess the
lowest number possible. And indeed, if everyone chose zero, the game would reach what’s known
as a Nash Equilibrium. This is a state where every player has
chosen the best possible strategy for themselves given
everyone else playing, and no individual player can benefit
by choosing differently. But, that’s not what happens
in the real world. People, as it turns out, either aren’t
perfectly rational, or don’t expect each other
to be perfectly rational. Or, perhaps, it’s some combination
of the two. When this game is played in
real-world settings, the average tends to be somewhere
between 20 and 35. Danish newspaper Politiken ran the game
with over 19,000 readers participating, resulting in an average of roughly 22,
making the correct answer 14. For our audience, the average was 31.3. So if you guessed 21 as 2/3 of
the average, well done. Economic game theorists have a
way of modeling this interplay between rationality and practicality
called k-level reasoning. K stands for the number of times a
cycle of reasoning is repeated. A person playing at k-level 0 would
approach our game naively, guessing a number at random without
thinking about the other players. At k-level 1, a player would assume
everyone else was playing at level 0, resulting in an average of 50,
and thus guess 33. At k-level 2, they’d assume that everyone
else was playing at level 1, leading them to guess 22. It would take 12 k-levels to reach 0. The evidence suggests that most
people stop at 1 or 2 k-levels. And that’s useful to know, because k-level thinking comes into
play in high-stakes situations. For example, stock traders evaluate stocks
not only based on earnings reports, but also on the value that others
place on those numbers. And during penalty kicks in soccer, both the shooter and the goalie decide
whether to go right or left based on what they think the other
person is thinking. Goalies often memorize the patterns of
their opponents ahead of time, but penalty shooters know that
and can plan accordingly. In each case, participants must weigh
their own understanding of the best course of action against how
well they think other participants understand the situation. But 1 or 2 k-levels is by no means
a hard and fast rule— simply being conscious of this tendency
can make people adjust their expectations. For instance, what would happen
if people played the 2/3 game after understanding the difference between
the most logical approach and the most common? Submit your own guess at what 2/3
of the new average will be by using the form below, and we’ll find out.

100 thoughts on “Game theory challenge: Can you predict human behavior? – Lucas Husted

  1. Add your guess to this form— don't post it in the comments! http://bit.ly/GameTheoryChallenge2
    And we'll post the result in the community tab in two weeks! Subscribe and turn on notifications if you don't want to miss the reveal!

  2. 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

  3. I'm confident that others will think like me so even after learning how to play the game and 0 being the only perfect option anyone guessing higher than 0 is going to win the game if at least few others think the same way. This is way to hard to predict it is more than just logical thinking it is more about the actual average stupidity vs the generally assumed average stupidity.
    This hurts my brain more than it should

  4. I hate this I hate that I can't know how others will reason even though we share the same knowledge I hate that being two steps ahead is not good and I hate not knowing what fraction of people will go with the common or the logical thinking. Nice video

  5. All I remember from game theory lectures in college is goalie. And till 3:44 of this video, I was freaking out where is the goalie?

  6. I think there is three possibilities:
    1. If people don't mind others also winning the game, then the answer would be 0. (I don't think this would happen);
    2. If people don't want others to win the game but knowing that the average K-level reasoning is 1-2, they will guess 18, then the answer would be 12. (But that won't be the case because knowing that others also know that they wouldn't choose 33-22);
    3. If people don't want others to win the game but know that others know about the k-level infographic, they'll assume that people will choose a lower number, and guees something between 1-4, then the answer would be 1-2. (This looks like real human behavior, thus i think it's the right one)

  7. What if people don't guess 0 because as long as there is a few people who guess something above 0, the correct answer is shifted up above 0?

  8. 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.

  9. What smell is this? Did someone burn something?

    Oh, nevermind that's just my brain trying to comprehend this.

  10. everytime i watch a ted ed video (especially those about paradoxes) i just end up being more confused than ever

  11. "so if you guessed 21… Well done"
    Me: "I was calculating that for the past 24 hours..! and I don't even get a fricking award… Screw this!"

  12. I think I am not understanding the object of the game. Given enough people, the average number guessed would ~50, hence the answer would be 34. If I know that someone else is thinking the same way, why would I even move off that number? @2:32 The average guess for the TEDEd audience is 31.3, which would be in the margin of error of 2/3 of ~50. Why would the correct answer now be 21?

  13. A lot of k-level thinking occurs in Poker. K-0 – Look at my holdings and odds of making your hand. K-1 – Putting someone on a range of cards and then make a determination if that range will make them. K-2 I know that my opponent is putting me on a range of cards based on pre-flop action, hence I would take an unorthodox line in the hand to disguise my hand. K-3, a 2nd opponent is in the hand and is raising the first guy , is he raising because he thinks the first person is bluffing? etc. etc.

  14. You guys have a very bad way of explaining a simple concept remember most of this is for young adults , its convoluted at best , "if the average half of 2 thirds of a half of an average is a half of a half of 2/3 of pi" …. when you can simply say what do you think will be 2/3 of the avg answer

  15. “You fell victim to one of the classic blunders. The most famous is never get involved in a land war in Asia; and only slightly less well known is this: Never go in against a Sicilian, when death is on the line!”

  16. This question actually don' really have an answer. Or so. The thing is the higher the range of numbers the more complicated the answer.
    If the range is 0 the answer should be 0. If the range is 1 the answer should be 1 since we will round 2/3 to 1. The more choices you have for a number it gets complicated. Probably just range after 10 it would really hard to come with the answer. Also the number of people guessing. Like say if you only have 2 persons and your range is from 0 to 2. They probably won't still get the answer. Not unless they both choose 0 or 1. Maybe the question should be given a range from 0 to 100 guess the number closest to the average guessed number. Just thinking.

  17. 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.

  18. I'm K negative.. because there is category group of people who didn't understand the question itself…?🤔…includes myself🙄

  19. I don't get it. The first step i understand (1/3 of 100 66,6), but how do you apply the same logic to go lower? It doesn't make sense at all. Nobody shouldn't guess higher than 67 i get that. But why should you go below that? Why does it make sense to mutiply 67 with 2/3, then 45 with 2/3 and so on?

  20. I like how Ted-Ed is literally testing our behaviour..
    First a guessing game with varied k-levels and only common knowledge provided. Now that Ted-Ed and "WE" know what the result was for that.
    Now, It's trying to see how we predict the answer in 'now new game with same rules' but with the information of one trial of it given to us.
    Does our K level rise individually or do we see a shift in thinking perspective…
    Classic, Ted-Ed being Ted-Ed

    P.S. I personally think now that most of know the previous result and judging by it (k level 3 btw) I guess this time the average would go a bit lower than before and hence the answer would too.. but who knows I maybe wrong.

  21. 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 »

  22. Now we all can achieve a new Nash Equilibrium by guessing 22 as we are perfectly aware that only people who have watched this video will fill that form (Only One K level of reasoning needed).

  23. i am confused by "all numbers guessed". Did you ask people to write random numbers between 0 and 100, is that what "guessed" means here?

  24. The thing is, why should you stick to rules when you know that playing rational or totally logical gives you no advantage. Depending on K levels makes sense, but most people get 0 or 1 K levels before their brain melts and then they probably still randomize their answer, because they have to do something with the information that this is common knowledge.

    Since everything got explained in this video I go with the answer 9. I think most people will think enough to understand that the number was below 30 (22), but in the other research it was 14. Still most people are too lazy to calculate 2 thirds of 14 and go on from their, so i think the correct answer this time will be 9, which is 2 thirds of 14. Sticking to K level 0 or 1 or whatever it is, because don´t expect people to go further.

  25. 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.

  26. Isn't 1 also a nash equilibrium and a more natrual one? 100 67 44 30 20 14 10 3 2 1. 2/3 of 1 is ~0,667 which is closer to 1 than 0.

  27. Watching in real-time, thought 33, and then didn't want to put more effort into thinking. Rationalized with "expecting poeple to not be acting rational is rational". Done.

  28. I would say that many gas stations are build across the road because the threat of competition still gives a higher payoff (in profit) than not entering the market at all (no profit) so the opponent will always choose to set his business unless the incumbent can make a credible threat which would make the payoff of not entering the market better.

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