# Concept Exchange Society

## APRIL MEETING

Wednesday, April 16, 1997 6:30 pm

At Glenn Johnston's House.

Presentation: Marvin Chester

## The Sphinx, New York Taxi Drivers and Layers of Strategy

Pre-Meeting Notice:

I will simply report on two fascinating articles I recently read.
One is called "Perils of the Sphinx" written by Alexander Stille. It appeared in the February 10, 1997 issue of The New Yorker. The other is entitled "Taxi Drivers and Beauty Contests" written by Colin F. Cameron, Professor of Business Economics at Caltech. (Engineering and Science, Volume 60, No. 1, 1997, p.11-19)

REPORT ON THE MEETING

Seven present: Glenn, Meredyth, Jeff, Roger, Roberto, Curt and Marvin.

I gave each a piece of paper with this instruction: "Write down a number between zero and twenty. We will average the numbers you write down. The one whose number is closest to one-half that average wins this dollar." I generously laid the dollar down. "Write down the number you think will win."

The numbers came back: 2, 3, 3, 0, 7, 4 and 5.
Half the average is 1.75 so the number 2 won. It was Meredyth's selection.

This collection of numbers indicated a good strategic sense among us. All the numbers were under 10. By random selection among numbers not greater than 20 ten would have been the average - had there been no other conditions on the numbers. Half that average would be 5. So the path of reason might lead one to write down 5; half the average by random selection.

But there is another level of strategy. Others in the game might also think like you. They had the same instructions. They might all write down 5. So the average would then be 5. If that were so it would be best to submit half that or 2.5.

But then suppose the others all come as far as you did in your thinking. Then they would also submit 2.5. You would be better advised to choose 1.25.

This progression of thought leads finally to zero. Zero is the result for an infinite chain of strategy levels.

Human failings enter. For the others if not for you. You choose a number greater than zero because you expect others in the game not to pursue strategic thinking to its ultimate result. The choice of 2.5 presumes that on average the others will get to level one of strategy - choosing 5.

The same article (Engineering and Science, Volume 60, No. 1, 1997, p.11-19) dealt with an interesting finding about a presumption in economics called the Law of Supply: that between the options 'to sell at a high price' and 'to sell at a low price' the choice will always be the former.

Remarkably it's not so! New York taxi drivers do not sell their working time this way.
The Law of Supply implies that if hourly wages go up the number of hours worked would rise. If the hourly wage drops the working time should drop. The slope of the curve of wages vs hours worked should be positive. Among cab drivers it is negative. The analysis was possible because cab drivers work variable hours according to their choosing. And the detailed data on their behavior and remuneration are avilable for analysis in the form of cab meter records. By the Law of Supply the drivers should work more hours when the call for their services is high and less when there is a lull in the demand for cabs. This choice is available to them. Their earnings would be signicantly better if they used this strategy. But, in fact, they seem to govern their working time by another principle: quit working as soon as some target income is met.

Evidently people do not behave to their best advantage. Pscho-logic is a far greater motivation than mathematical logic.

The Sphinx and the Pyramids are holy relics in the mythology of various superstitious and mystical sects according to Alexander Stille's article in the February 10, 1997 issue of The New Yorker. The detailed study of these edifices reveals that they were the work of the local people living in the prosperous society of the time. People motivated by their belief system - their mythology. The research directly contradicts the New Age mystical mythology that they were built by space aliens to contain documents on the "secrets of the universe'. But people who believe myths are not bothered by factual findings. So, in adoration of the relic of their myths, they financially support the research which topples their myths.

A merry collusion for all.

April 1997
Marvin Chester
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