What’s 2/3 of the Average?

Here’s a well known and subtly interesting game. If it is new to you, ponder it for a bit of weekend fun. Or better, pose it to your friends and family. I’ll post analysis on Monday. Later on I’ll apply the analysis to the real-world issue of speculative bubbles in financial markets.

Suppose everyone in your town selects a real number between 0 and 100, inclusive (i.e. 0 and 100 are both possible choices, as is any other number between). The winner is the individual (or individuals) who selects the number closest to 2/3 of the average of numbers chosen. What number do you choose? Why?

Just to be clear, suppose there are three players who select the numbers 10, 20, and 30. The average is 20, and 2/3 of the average is 13.333… . Therefore, the winner is the individual who selected 10 because it is closest to 2/3 of the average.

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