“Consider a guess-the-number game in which players must guess a number between 0 and 100. The person whose guess comes closest to two-thirds of the average guess of all contestants wins. That’s it. And imagine there is a prize: the reader who comes closest to the correct answer wins a pair of business-class tickets for a flight between London and New York. The Financial Times actually held this contest in 1997, at the urging of Richard Thaler, a pioneer of behavioral economics. If I were reading the Financial Times in 1997, how would I win those tickets? I might start by thinking that because anyone can guess anything between 0 and 100 the guesses will be scattered randomly. That would make the average guess 50. And two-thirds of 50 is 33. So I should guess 33. At this point, I’m feeling pretty pleased with myself. I’m sure I’ve nailed it. But before I say “final answer,” I pause, think about the other contestants, and it dawns on me that they went through the same thought process as I did. Which means they all guessed 33 too. Which means the average guess is not 50. It’s 33. And two-thirds of 33 is 22. So my first conclusion was actually wrong. I should guess 22. Now I’m feeling very clever indeed. But wait! The other contestants also thought about the other contestants, just as I did. Which means they would have all guessed 22. Which means the average guess is actually 22. And two-thirds of 22 is about 15. So I should … See where this is going? Because the contestants are aware of each other, and aware that they are aware, the number is going to keep shrinking until it hits the point where it can no longer shrink. That point is 0. So that’s my final answer. And I will surely win. My logic is airtight. And I happen to be one of those highly educated people who is familiar with game theory, so I know 0 is called the Nash equilibrium solution. QED. The only question is who will come with me to London. Guess what? I’m wrong. In the actual contest, some people did guess 0, but not many, and 0 was not the right answer. It wasn’t even close to right. The average guess of all the contestants was 18.91, so the winning guess was 13. How did I get this so wrong? It wasn’t my logic, which was sound. I failed because I only looked at the problem from one perspective—the perspective of logic. Who are the other contestants? Are they all the sort of people who would think about this carefully, spot the logic, and pursue it relentlessly to the final answer of 0?”