Being One Step Ahead
Source: Are You Smarter Than Other New York Times Readers? by David Leonhardt and Kevin Quealy
A few weeks ago, the New York Times gave its readers an interactive puzzle with an answer that depends on everyone else’s answers. The goal is to predict everyone else’s answer, while they’re all trying to do the exact same thing. Everyone has to pick a number between 0 and 100 that they think is two-thirds of the average of all the numbers guessed. Getting the correct answer involves thinking about what everyone else is going to say.
If this was randomly done, then the average of numbers picked from 0 to 100 would be 50 and two thirds of that would be 33. However, these are New York Times readers, who have probably all reached this conclusion. So if everyone picks 33, then the correct answer becomes 22. One could technically keep continuing this thought process, and it eventually leads to 0. So the reader has to guess how many rounds of this thought process that other readers are likely to go through.
The bar graph of readers’ guesses is very interesting, but for the sake of not spoiling the puzzle, I will not reveal it. There are specific numbers where the amount of guesses spike incredibly. The areas with the biggest peaks were at 50, 33, 22, and 0-1. The people who picked 0 actually picked the Nash equilibrium for this puzzle. If everyone could see the guesses and had infinite tries, this would be the answer to the game.
However, two-thirds of the average of the guesses is not actually 0. This means that people are demonstrating “k-step thinking.” This means the amount of times someone will go through the thought process. For guesses like 50, 33, and 22, these people used k-step thinking with k as a relatively small number like one or two. Infinite steps would lead to an answer of 0.
It is apparently difficult for people to think multiple steps ahead. But in order to succeed in life, this skill is very important. The authors gave many different examples like the housing market and the stock market. In the stock market, the best company might not be the most profitable. The most profitable is the company that others think will be the best company. So in this field, everyone is always trying to outwit each other and be one step ahead. Although examples of this are visible in our lives everywhere.
(side note: I found out about this puzzle from my Physical Chemistry class)