# Musical Chairs

In September, 1982, railroad engineers across the United States went on strike for several days until the President signed a bill ordering them back to work. The strike created transportation difficulties in several major cities, including Chicago, as suburbanites who normally rode the train sought alternative ways to get to work. Many found that highway congestion was not as serious a problem as was parking-lot congestion. When they finally got downtown, there were no parking spaces left. After reporting the problem, one television newscaster in Chicago advised all commuters to start driving earlier the next day so they would find a spot to park.

If all commuters had followed this advice, the situation would have been worse rather than better. The parking lots would have filled up earlier and the same number of people would have been unsuccessful in finding spots. Everyone would have wasted time by starting earlier. The situation here is not unlike the proverbial fire in the theater. If everyone calmly walks to the exits, the theater will be emptied as fast as, if not faster than, if everyone runs to the exits. What may be a solution for one is not a solution for all if everyone tries it.

As another example of a matching problem, consider this excerpt from a letter that many thousands of people have received:

"You too will be making easy money in three to four weeks...My method is simple. I sell thousands of people a product for \$5.00 that costs me pennies to produce and mail. Everyone involved in the program makes money from everyone else in the program. If anyone makes money, everyone makes money...This plan has the effect and appeal of a chain letter, but it is legal since you are offering a legitimate product to your people."

The product being sold is a copy of instructions that the buyer then can sell to others.

Is it possible for everyone involved to make money from this scheme? To see that it is not, you must first realize that because the "product" being sold is worthless, the scheme is simply a way of redistributing money. It works with the same logic as a chain letter. All the money that people make in the scheme must come from others involved in the scheme. The sum of money received must equal the sum of money sent. The redistribution is the same as that which takes place in a poker game: the sum of winnings must equal the sum of losings. If anyone involved in the game ends up with more than he started with, someone else must end up with less. (These are zero-sum games--the sum of all winnings and all losses equals zero.)

In matching problems, there is no need for any assumptions of how people act; the results are determined regardless of how people behave. Economists do use matching formulas, but never alone as a complete theory. Economic theories always contain assumptions about how people act. But within the theories, matching formulas in the form of identities can play important roles. An identity is a statement true by definition. An example of an identity is the statement, "The amount bought must equal the amount sold." Because whatever is bought must have been sold and vice versa, this statement must always be true. Another example of an identity is the statement "Net worth equals assets minus liabilities." This statement underlies the balance sheet, a basic tool of accounting.

Next we discuss contingent behavior.