"Guess 2/3 of the average" game results [conducted among CC-related people]

[dektox]

The experiment we conducted is related to the Keynesian beauty contest which was devoted to explain the price fluctuations in equity markets. Keynes described the action of rational agents in a market using an analogy based on a fictional newspaper contest, in which entrants are asked to choose the six most attractive faces from a hundred photographs. Those who picked the most popular faces are then eligible for a prize.

A naive strategy would be to choose the face that, in the opinion of the entrant, is the most handsome. A more sophisticated contest entrant, wishing to maximize the chances of winning a prize, would think about what the majority perception of attractive is, and then make a selection based on some inference from his knowledge of public perceptions.

Keynes believed that similar behavior was at work within the stock market. This would have people pricing shares not based on what they think their fundamental value is, but rather on what they think everyone else thinks their value is, or what everybody else would predict the average assessment of value to be.

Later on, the experiment was upgraded to so-called “guess the average game” that has been conducted several times on different audiences including the audience of Financial Times readers [Richard H Thaler, 1997. The average guess was 18.91].

We decided to check if the answers of those who are interested in cryptocurrency issues differ from the known audiences’ answers. We’ve conducted the experiment with 2 audiences: “LinkedIn cryptocurrency-related people” and “traders of one of the Ukrainian exchanges”.

We’ve asked following question:
“Guess a number from 0 to 100, with the goal of making your guess as close as possible to 2/3 of the average guess of all those participating in the contest. (To help you think about this puzzle, suppose there are three players who guessed 20, 30 and 40 respectively. The average guess would be 30, two-thirds of which is 20, so the person who guessed 20 would win)”

The prize for the closest guess for the 1st audience was 0.1 ETH and 10 KRB for the 2nd audience.

From the 1st audience, we’ve received 643 answers. The average guess is 30.19 and the winning number is 20.13. The winner answered “20.1”, which differentiate him from 29 people who answered “20”. The answers distribution is given below:



From the 2nd audience, we’ve received 310 answers. The average here is 39.74 and the winning number is 26.49 (which is more than 6 points above the winning number for the 1st audience and almost 14 points above the Financial Times readers winning number—12.6).

There are 6 winners who tie with the answer “27”. We’ve contacted them in order to proceed with the payment. The distribution of answers is given below:



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Most of the participants are the 1st level depth of reasoning and the winners are the 2nd level depth of reasoning, unlike the audience of Financial Times readers from Thaler’s experiment (they are 2nd and 3rd levels correspondingly).
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We would appreciate your comments:
Why have you chosen this specific number?
What do you think justifies such a big difference?

You can also participate in the so-called second round among those, who are acknowledged with the results here: https://goo.gl/forms/ReqIeE32ynIOAgMj1

[odolvlobo]

Interesting. The value indicates expectation with a higher value meaning lower expectation.

So, another question is how well the expectation matches the reality. My interpretation of the results based on my familiarity with the people in this environment, is that it accurately demonstrates the level of knowledge about economics (more specifically game theory) by the groups in the contest. My own guesses would have been 22 for the linkedin group and 34 for the traders.

[dektox]

Interesting. The value indicates expectation with a higher value meaning lower expectation.

So, another question is how well the expectation matches the reality. My interpretation of the results based on my familiarity with the people in this environment, is that it accurately demonstrates the level of knowledge about economics (more specifically game theory) by the groups in the contest. My own guesses would have been 22 for the linkedin group and 34 for the traders.

odolvlobo, in order to study how the expectation matches the reality, we've come up with this traders analysis. We are comparing their trading performance with the answer's accuracy. I will send full research to you since it is ready, but here is the spoiler: there are about 1/4 of traders who perform well in trading despite their bad answers. 

[zachamo]

Thanks for the follow-up! Trying to remember my response to this one.. I think it was along the lines of 18.73 :p

[dektox]

Thanks for the follow-up! Trying to remember my response to this one.. I think it was along the lines of 18.73 :p

zachamo, the user who has specified email that is very similar to your nickname has answered 18.73 on 24.11.2017 15:43:40 (GMT) :-)

So this user [you] was so close to the Thaler's experiments average which is 18.91 (but not close to the Thaler's experiment winning answer)

[LeeFox]

after calculating that more than 67 can not be, the first thought was about the figure 33. with the answer was in no hurry. 33 this is as it would simply be. so I stopped at 27

[dinofelis]

Wow.  I guess this indicates the extremely low mathematical background that most of the players have, or assume of their peers - which in itself is an element which is difficult to take into account: how DUMB are the co-players ?

If you ask me to guess, in a set from 0 to 100, to be as close as possible to 2/3 of the average, and I consider that the others are *like me*, then the answer is evident, and everyone wins:  zero.  It is a Nash equilibrium in this game !

Why ?  Let us assume that the playing agents think that the answer should be X.  If the playing agents think that the other playing agents are as smart as he is, they will also find X on average.  But then the good answer is 2/3 X.  But there's no reason then, why intelligent agents should pick X: they want to win, and pick all of them 2/3 X.  But then the average is 2/3 X.  So the winning answer is (2/3)^2 X.

Now, you quickly understand why agents will go through that iteration N times, and will find (2/3)^N X.  In order to win, you should replace N by N+1.  But if you repeat that, you'll end up by reaching infinity.  And then you have 0.  And guess what ?  If all agents guess 0, then they all have won too, because 0 is also 2/3 of 0.

If the average, in this game, is 33, then this means that on average, people can only reason one single step and are not able to iterate recursively.  Indeed, you take the other people for total first-order dumb asses, you think they will say just anything, and their average is then 50.  In a perfectly dumb setting, the average would be 50, and the winning number would be 33.  Now, you think that most people have just a single brain cell, that can think this, that the others are complete dumb asses, and that they are way way smarter, so they think that people will say "50" and so they say 33.   If the average IS 33, that means that most people take their peers for total dumb-asses, but can think one step ahead.

I would have said 0.  But it seems that it is much more favourable to assume that most people think that others are complete morons ; or that most people think that most people think that others are complete morons.  

I can start to see why crypto-pyramid games have such a success !

[dektox]

Wow.  I guess this indicates the extremely low mathematical background that most of the players have, or assume of their peers - which in itself is an element which is difficult to take into account: how DUMB are the co-players ?

If you ask me to guess, in a set from 0 to 100, to be as close as possible to 2/3 of the average, and I consider that the others are *like me*, then the answer is evident, and everyone wins:  zero.  It is a Nash equilibrium in this game !

Why ?  Let us assume that the playing agents think that the answer should be X.  If the playing agents think that the other playing agents are as smart as he is, they will also find X on average.  But then the good answer is 2/3 X.  But there's no reason then, why intelligent agents should pick X: they want to win, and pick all of them 2/3 X.  But then the average is 2/3 X.  So the winning answer is (2/3)^2 X.

Now, you quickly understand why agents will go through that iteration N times, and will find (2/3)^N X.  In order to win, you should replace N by N+1.  But if you repeat that, you'll end up by reaching infinity.  And then you have 0.  And guess what ?  If all agents guess 0, then they all have won too, because 0 is also 2/3 of 0.

If the average, in this game, is 33, then this means that on average, people can only reason one single step and are not able to iterate recursively.  Indeed, you take the other people for total first-order dumb asses, you think they will say just anything, and their average is then 50.  In a perfectly dumb setting, the average would be 50, and the winning number would be 33.  Now, you think that most people have just a single brain cell, that can think this, that the others are complete dumb asses, and that they are way way smarter, so they think that people will say "50" and so they say 33.   If the average IS 33, that means that most people take their peers for total dumb-asses, but can think one step ahead.

I would have said 0.  But it seems that it is much more favourable to assume that most people think that others are complete morons ; or that most people think that most people think that others are complete morons.  

I can start to see why crypto-pyramid games have such a success !

dinofelis, yeah, we faced this confusion before:
people smart enough to find Nash equilibrium often even can't imagine that others would pick any different from 0 number;-)

I asked myself with the question "So what? Why should I care about results?

The answer could be as follows: the winning strategy to outperform trading fellows would be the 2nd level reasoning, so it makes sense to make 2 iterations to beat the [average] player. So, when I chose, for example, next Fibonacci level [or what they all use], I know that everybody looks on this Fibonacci level, the price hardly reach it because of massive sell at this point, so I place my sell order a bit lower [but everybody place an order a bit lower], so I place my order a bit lower from a bit lower :-)

As for the low mathematical background of market players. I found this research in the Thaler's book "Misbehaving". In chapter 21 he gives results of the same research conducted among Financial Times readers. I think you would like one of his comments [note that Financial Times readers have shown the 3rd level of reasoning]:

"At least three people who guessed 33 reported having used the random number generating function in Excel to determine that, if people choose at random from 0 to 100, the average will be 50! Maybe I have too high hopes for the mathematical sophistication of Financial Times readers, but I would have thought they could figure out that the average of a number picked at random between 0 and 100 is 50 without using Excel. This confirmed my longheld suspicion that many people use spreadsheets as an alternative to thinking"

[dektox]

after calculating that more than 67 can not be, the first thought was about the figure 33. with the answer was in no hurry. 33 this is as it would simply be. so I stopped at 27

Wow! The winner is here. Have you contacted us back on the
exchange?

[dektox]

New results will come shortly

[dektox]

Currently, we are conducting a LinkedIn research, now with the rest of the world (except the USA). It does take more time than we planned initially.

[Nadia_l]

So dektox what was the results???
I really like this theory with such mind games and think that they are used in all markets that are manipulated by some people, which one can call whales or by other names.
And they are acting due to the analysis of what the crowd does, by issuing the fake or even real news in the definite order.
What do you think?
Your parallels of how this is acting in the crypto market with their well known and widely-spread "next Fibonacci level" is very close to the truth, IMO.
Do you think that the safe choice in this situation is not to react to the fud and news but as they are spread in order to make the impact on the trader choice in the appropriate time?  
As my friend advised me: Just by some coins/tokens and wait when they will be in the top of the biggest movers list and then sell and vice versa.

[dektox]

So dektox what was the results???
I really like this theory with such mind games and think that they are used in all markets that are manipulated by some people, which one can call whales or by other names.
And they are acting due to the analysis of what the crowd does, by issuing the fake or even real news in the definite order.
What do you think?
Your parallels of how this is acting in the crypto market with their well known and widely-spread "next Fibonacci level" is very close to the truth, IMO.
Do you think that the safe choice in this situation is not to react to the fud and news but as they are spread in order to make the impact on the trader choice in the appropriate time?  
As my friend advised me: Just by some coins/tokens and wait when they will be in the top of the biggest movers list and then sell and vice versa.

Hi Nadia, the results are in the original post. It was updated. Briefly, most of the cryptocurrency traders (that took part in the survey) are the 1st level depth of reasoning and the winners are the 2nd level depth of reasoning, unlike the audience of Financial Times readers from Thaler’s experiment (they are 2nd and 3rd levels correspondingly).

As for your questions, despite the experiment was interesting, there is no evidence that certain behaviour (in regards to the level of reasoning) can lead to higher profits. Please find below the distribution of profits by guessed numbers: