Puzzle

I've run into a behavioural economics puzzle a couple times over the last few weeks. I'm posting it now because I have just ran across a wonderful graphic illustrating how real people tried to "solve" the puzzle.

The following takes material from a posting by John Mauldin (I believe Mauldin took it from the following a 2004 research paper James Montier):

Ask people to pick a number between 0 and 100, and telling them the winner will be the person who picks the number closest to two-thirds the average number picked.

Here is a chart of the guesses made by 1000 professional investors:


Here is Mauldin's commentary on the above guesses:

The highest possible correct answer is 67. To go for 67 you have to believe that every other muppet in the known universe has just gone for 100. The fact we got a whole raft of responses above 67 is more than slightly alarming.

You can see spikes which represent various levels of thinking. The spike at fifty reflects what we (somewhat rudely) call level zero thinkers. They are the investment equivalent of Homer Simpson, 0, 100, duh 50! Not a vast amount of cognitive effort expended here!

There is a spike at 33 - of those who expect everyone else in the world to be Homer. There’s a spike at 22, again those who obviously think everyone else is at 33. As you can see there is also a spike at zero. Here we find all the economists, game theorists and mathematicians of the world. They are the only people trained to solve these problems backwards. And indeed the only stable Nash equilibrium is zero (two-thirds of zero is still zero). However, it is only the ‘correct’ answer when everyone chooses zero.

The final noticeable spike is at one. These are economists who have (mistakenly…) been invited to one dinner party (economists only ever get invited to one dinner party). They have gone out into the world and realised the rest of the world doesn’t think like them. So they try to estimate the scale of irrationality. However, they end up suffering the curse of knowledge (once you know the true answer, you tend to anchor to it). In this game, which is fairly typical, the average number picked was 26, giving a two-thirds average of 17. Just three people out of more than 1000 picked the number 17.

I play this game to try to illustrate just how hard it is to be just one step ahead of everyone else - to get in before everyone else, and get out before everyone else. Yet despite this fact, it seems to be that this is exactly what a large number of investors spend their time doing.

The completely rational answer is zero. But if you choose zero you will lose because not everybody is rational. To play this game effectively you have to recognize the limits on most people's thinking. You have to anticipate their errors. So there is no completely rational answer. Similarly the EMH (Efficient Markets Hypothesis) is wrong because it demands a level of rationality beyond what people actually exhibit.