Game Theory

I think my last posted really touched on some interesting game-theory topics.

Then, coincidentally, I check Slashdot and see the following poll (I’ve modified it, removing a silly answer that’s included in every poll):



How’s that for a stumper?

Obviously, 0% can never be the right answer. If someone votes for it, it can’t be true. So we can immediately dismiss that one as the right answer.

100% COULD be true if everyone voted for it, but that assumes that everyone will be perfectly cooperative, which is unlikely. Note that if any single person deviates from that state of perfect cooperation and votes for 1%-25%, they would then be correct and everyone who voted for 100% would now be wrong. So it’s probably unlikely that 100% would win.

If the votes were randomly distributed across all choices, we should expect that 1%-25% would be correct, since 100% divided across 6 choices would mean each choice would get about 17% of the votes. But we can assume that everyone voting in the poll isn’t just a robot, but a rational human being, thinking along the same lines we do. If enough people thought that everyone ELSE would vote more or less randomly, then the 1%-25% choice would grow disproportionately large. But if enough people thought along those lines, they might vote for something else, which could make 1%-25% correct again.

I find stuff like this absolutely fascinating.

This led me to do some reading on game theory (thank you very much, Wikipedia!), and I came across an article describing the “Keynesian beauty contest”. The story is that there was a contest in a London newspaper where 100 female faces were shown, and entrants were asked to choose six faces that were the “most beautiful”. Entrants who chose the most popular choice would get entered into a raffle to win a prize.

If you were in this situation, what would you do? Voting for the six faces you find most attractive might work, but is a little naïve, since your tastes might be sort of individual. A more sophisticated approach might be to try to guess what the general perception of beauty is, and pick the six faces that match that. But, it’s probably safe to assume that others are thinking along the same lines, so maybe it’s better to try to guess what everyone else thinks everyone ELSE thinks of as the general view of beauty. And this can be carried on to the next order, and the next.

So what? “Keynes believed that similar behavior was at work within the stock market. This would have people pricing shares not based on what they thought their fundamental value was, but rather based on what they think everyone else thinks their value was, or what everybody else would predict the average assessment of value was.”

Simple games can reveal quite a lot. Exactly why is it that 100% is a bad choice in the above poll? What does that tell us about human nature? During rush hour, how do I choose the least populated route? Isn’t it possible that others might choose that same route, thereby making it the worst choice? When is the best time to go to the post office?

I think that’s why I enjoy certain board games so much. They are a tiny microcosm of some pretty vast social, biological, and economic ideas. Good, good stuff.