What is this game doing in a museum of economics? Although it may not seem very relevant at first, this game is a pretty good simulation of the psychology of the stock market. After all, when buying stock, one attempts to anticipate the price others are willing to pay.
Additionally, this game is an introduction to some of the basic concepts of game theory. It gets you, the player, to think in ways common to game theory ("I think that they think that …"). It also demonstrates the tension and difference between real-life behavior and theoretical analysis.
The "rational" guess for this game is zero. The reasoning is something like this: If I think that you will guess 100, then I should guess 66. However, if I think I should guess 66, then you would also think that I should guess 66, which means that you should guess 44. That means that I should actually guess 29, and so on and so forth. Thus, if you continue through this line of reasoning, ultimately, the only answer that makes sense is zero.
If you didn’t guess zero, though … don’t worry too much. This game is also an example of how real life doesn’t always match up with theory. Studies with large groups of college students have resulted in averages where the winning number was 24 (and no one chose zero for an answer). A similar experiment with the readers of a financial newspaper had a winning average of 13.