HAVING FUN WITH MATH

This is the final part in my series this week about education.  In an earlier blog I mentioned how I am a member of Mensa.  Today I will educate you about that group.


To become a member of Mensa, the oldest high IQ society in the world, one must score at the 98th percentile or higher on a standardized, supervised IQ or other approved intelligence test. Mensa's constitution lists three purposes for its existence: "to identify and to foster human intelligence for the benefit of humanity; to encourage research into the nature, characteristics, and uses of intelligence; and to provide a stimulating intellectual and social environment for its members.”


To fulfill one of those goals, today I will endeavor to “foster human intelligence” by sharing one of my favorite non-zero sum sequential games; the $1 bill auction. Trust me, it might sound boring, but this will be fun! I am changing the denomination of the game to $20 to make it even more interesting.

This auction was game created by economist Martin Shubik to explain rational thought theory. This is defined as when people have perfect information but are compelled to make irrational decisions based totally on a sequence of rational thoughts.

I stand up in a random group of people and announce that I am auctioning off a perfectly legal $20 bill. How much will you bid for it? The only difference here from a regular auction is that the losing bidder also has to pay the price of their bid.

You quickly bid $1 and anticipate your $19 profit hoping no one else gets in the game. But somebody else jumps in and bids $3! So you bid $4. A third person shouts out $5 and your anger at their arrogance to try to outbid you causes you to go to $6. Have you figured the game out yet? Unless the bidding stops at a low level, the only winner will be the auctioneer. Even if you bid $19 and everyone else stops, the auctioneer will get your $19 plus the losing bid and will collect more than the original $20.

The only theory under which the auctioneer loses is if the audience is in collusion with each other and only one person bids and then stops. But because the game was played randomly, no one in the crowd really has the chance to figure the game out.

So we had all the information at the beginning: someone is auctioning off a $20 bill, but we never stopped to pay attention to the second part of the game-- that the losing bidder had to pay also.

If I had not been stimulated intellectually by being in honors classes, I would have found school boring and my knowledge would have been achieved at the level of the slowest learning student instead of at my pace. I would be lucky to just know how to add one and one instead of understanding game theory.

It is obvious that school officials are making irrational decisions in eliminating honors classes and changing the grading system. I thought this topic was so important, I wrote about it three times.  Maybe this time will be the charm.