The most successful investors are those who can accurately assess the general sentiment of other investors and then stay one step ahead of the rest.

Logic doesn’t work

Economists have taken a cue from Keynes and modeled this sort of problem what’s often called a beauty contest game. I give you the following game: you and nine other players, each must choose a number between 1 in 100. The winner of the game is the one whose number is closest to two thirds of the groups average, so if average of the group or 60

There is someone whose choice was near 40 would be a winner. Now let’s use a backwards induction to try to solve this game. You might expect that the average of 10 random numbers would be around 50 so you should choose 33 which would be two thirds of that average. But, wait the other players are rational just like you they know that.

They should pick 33 so to outsmart them you only depict two thirds of that for 22. But, wait again the others know that too they’ll pick 22 so you need to pick two thirds of that and so if you follow this logic to its conclusion then everyone should pick the smallest number possible one.

That’s a solution to the skin and it never happens. Whenever groups of people have played this sort of beauty pageant game in the laboratory they never all agree on the same number. They give a range of numbers the average of which is usually in the 20s or 30s. This means that people on average only follow one or two steps of backwards induction.

Optimal choices in real world

They think I know that they know that I know but not much more than that. And who wins the game? the best strategy isn’t the rational solution to the game, it’s one more step than the rest of the group. If the groups average of 33 then you win by choosing 22 but the groups average for 20 you only win if your answer were around 14.

The key idea here is that optimal choices in real world games depend on your assessments of the rationality of the other players and you can use your own limitations as a good guide to the limitations of the others. Think back to the stag hunt game I introduced a few minutes ago.

Suppose that there were 10 hunters in your group if everyone cooperates each get a big reward. Now imagine yourself walking toward the center of the forest, what might you be thinking? You know that the others might be tempted by the sure thing small reward and you know that each of them is thinking the same thing.

Everyone recognize that there’s some risk that someone will fail to cooperate, either because of temptation or just a mistake. In this case your own doubt might be a good guide to others doubt and to the likelihood that at least one person will cooperate so you switch your choice to the safe option just like many of the others.

Decision processes have limitations

We don’t have the computational abilities to reason through all the steps of a complex decision problem, to return to an idea from an earlier article, we have bounded rationality. Bounded rationality means that our decision processes have limitations. We don’t approach these games in a mathematically optimal way.

Instead we approach problems in a way that’s suited to our own confrontational limitations and that tries to take advantage of the structure in the world around us. One very powerful tool for using the structure in our world is to look for a focal point. Before I define a focal point let’s play a game, one I’ve adapted from similar games proposed by the economist and Nobel Laureate Thomas Schelling.

You’ve been selected to be one of two participants in American game show. You will win $10 million if you can shake hands with your fellow participant at a particular place date and time somewhere in the United States, during the next calendar year. You will have to write down your place, date and time right now and your partner is a random American adult who has the identical instructions and is doing the same thing.

If your locations do not match then neither view wins anything good luck!  I want you to think from a what place would you pick what date and what time? Now hold on your answer for a moment. Let’s think about how many places there are in the United States. The number is so large that coordination by random chance is essentially impossible, even before you add the additional challenge of agreeing on the right day and at the right time.

Cooperative markets

So we should expect that you and your fellow contestant would never win the game show, you’d be much more likely to each draw lottery ticket and have the same set of numbers. But when I run this game in my classes without the promise of a jackpot I usually get the same answers.

Students say Times Square New York City January 1 midnight or they say stature liberty July 4 noon or the White House or US capital usually on July 4 at noon. Any answer is possible but a few answers are much much more probable than the rest. Shelley called those answers focal points.

Focal points have special properties that distinguish them from other choices and thus they facilitate coordination even when people can’t communicate directly. Let’s consider another example one you could test yourself. Suppose that you and a friend have to coordinate your behavior by each selecting o1 coin from a bag of 100 coins independently.

If all 100 coins are pennies you are really unlikely to select the same one, but if 99 of the coins or pennies and one is a nickel I’m completely sure you’ll be able to coordinate. That one meaningful outlier is a focal point. Focal points turn out to be extraordinarily important for real world markets, they can change competitive markets into cooperative ones which can be very bad for consumers.