Can you solve the riddle of the Keynesian beauty contest?

You should always be suspicious when a game theorist suggests “a bit of fun”.

It’s usually something to catch you out.

Like the one where they tell you, “A cricket bat costs £1 more than a ball. Both together cost £1.10. How much does the ball cost?”

(In case you haven’t seen that one before, the answer isn’t 10p. You can click here for the right answer.)

Well, here’s another one that market analysts are pretty keen on …

1. Everyone playing the game secretly submits a number from 0 to 100.

2. All entries are collected and the guesses are averaged together.

3. The winning number will be chosen as two-thirds of the average. The entry closest to this number wins the prize.

Got it?

Now, have a think about what number you’d chose.

Write it down. Even better, click “reply” on this email and send me your answer – then we’ll really be able to put this to the test.

Now, if you’re a maths-head, you may have already worked out the logical answer to this problem.

Your reasoning might go something like this …

Assuming people chose randomly between 0 and 100, the average will be 50, and two-thirds of 50 will be 33.3 … But then, everyone will be thinking this, so they will all chose 33.3 … so two-thirds of 33.3 is 22.2 … but they’ll all be thinking that, too, so two-thirds of that is 14.8 … 9.9 … 6.6 … 4.4 … and soon you’ve reached the answer of 0.

So, our super-rational mathematician will write down “0”, confident of winning the prize.

However, most of us aren’t “super-rational mathematicians”!

In fact, a surprising number of people will even put down answers to this question that are higher than 66 – these are numbers that could never win.

Why?

Because it’s a lucky number, or because they weren’t thinking it through, or just took a guess.

If you want to know the right answer, click here.

This game is sometimes called the Keynesian Beauty Contest.

It’s based on economic theory of Maynard Keynes that stockmarket investments are like newspaper beauty contests. By this he meant that people price shares based not on what they think their fundamental value is, but instead on what they think everyone else thinks their value is.

So, when assessing who’ll win the newspaper beauty contest, people aren’t judging the person they find the most beautiful, but the person they believe that the majority of people will find beautiful.

And this is exactly what investors are doing when they look at the stockmarket. Instead of judging the shares they like the best – they want the ones that they believe everyone else will like best.

There is a theory about markets that our “super-rational mathematician” would like. It says that markets are inherently rational. It’s called the “efficient market hypothesis”, and incredibly is still taught to many economics and business students as fact.

It goes something like this …

Financial markets are efficient …

… information (i.e. the fundamentals) flows freely …

… investors make rational decisions based on that information.

The reality is, however, that people make downright terrible, irrational decisions all the time.

For example, I have just ordered a wildly overpriced rug for my living room, which should be delivered about 10 days before the arrival of my new puppy.

Stupid, stupid, stupid.

However, the whole investment game hangs on the belief that we can make better decisions than others. And if we didn’t believe that we could outsmart other people, then we wouldn’t be in the game of trying to make money from the markets.

We’re always hoping to buy low, so we can sell to someone stupid enough to be buying high.

The belief that we’re making better decisions than others is what makes the markets go round.

No doubt, it’s why the world of investment is littered with egomaniacs!

Until next week,

Mark Rose

Answers

• The bat costs £1.05 and the ball costs 5p.

• Unlike the bat-and-ball question, there is no “right” answer for the two-thirds of the average game – it depends on how far individual members of the group “think through” the problem. When played in real-life situations, the winning answer is usually somewhere between 20 and 30. A fair distance from the “correct” rational response of zero.

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Be wary of your heroes. This is what REALLY makes a good trader How to behave badly and get away with it