Games People Play: War to Used Cars

October 16, 1994|By RICHARD O'MARA

Whoever it was who said it doesn't matter if you win or lose but how you play the game, missed the point. It matters very much.

According to game theory, it's how you play the game that usually determines whether you win or lose.

You don't make a move in chess without first trying to figure out how your opponent will react to it.

Game theory assumes that all human interactions, personal, institutional, economic, can be understood and navigated by presumptions similar to those of the chess player. The theory has been around for almost two centuries.

Last week it received the ultimate recognition as an established and significant concept in economics. Three of game theory's top exponents were awarded the Nobel Prize in economics.

They are John F. Nash of Princeton University, John C. Harsanyi of the University of California at Berkeley and Reinhard Selten of the University of Bonn in Germany.

They will share the $930,000 cash prize.

The award illustrates how long it sometimes takes for the Nobel committee to catch up with trends and ideas in certain disciplines. The economics prize was established only in 1968, a quarter-century after game theory was elaborated in modern times.

This was done in the mid-1940s by John von Neumann and Oskar Morgenstern in their book "The Theory of Games and Economic Behavior."

Game theory is both easy and excruciatingly difficult. People use it all the time, average people, in their daily lives. It comes into play in mundane deals like buying a car, where a certain skill in haggling is required.

The buyer's offer is usually formulated on the basis of what he or she presumes the seller will take. The seller is guided by a presumption about how high the buyer will go.

The outcome of this negotiation could be totally positive (if the deal satisfies both parties), totally negative (if it falls through), or positive for one party and less so for the other (depending on how much is paid.)

Game theory is defined by economists Avinash Dixit of Princeton and Barry Nalebuff of Yale as "the science of strategy." It is used to describe any relationship and interaction, economic, social or political. And it's useful in creating strategies for negotiators.

It can help you win, and that is why companies and governments hire game theorists to write strategies against other players in whatever game they're in. Mathematics and statistics are the tools they use.

'Nash equilibrium'

Professor Nash, 66, was only a graduate student when he formulated the "Nash Equilibrium," the theory cited for the Nobel Prize.

His equilibrium can occur, say, in a marketplace when no matter what the participants do they cannot improve their situation, either by raising or lowering prices, or by increasing or decreasing output.

They have reached this equilibrium by pursuing their individual interests.

A similar situation arises in "Tosca," Puccini's opera. It's an example Joseph Harrington likes to use in his classes at the Johns Hopkins University.

Dr. Harrington is an expert on game theory. He sees an example of a Nash Equilibrium in the actions of two of the opera's principal characters the singer, Tosca, and the villainous police chief, Baron Scarpia.

Scarpia has Tosca's lover, Cavaradossi, arrested, and threatens execute him unless Tosca accedes to his sexual advances.

Consider the desires and choices of Tosca and Scarpia, said Professor Harrington:

"Scarpia wants Tosca's sexual favors. He tells Tosca that if she comes across he will order the firing squad to use blank cartridges on Cavaradossi. Tosca then has to decide to give in to Scarpia or stab him to death."

The two principals have primary and secondary aims, Professor Harrington points out:

"Scarpia cares most about Tosca's sexual favors. Secondarily, he would prefer to see Cavaradossi dead.

"Tosca cares most about Cavaradossi living. Secondarily, she would like to stab Scarpia to death."

The two try to fulfill both of their aims. Scarpia secretly orders his men to use live ammo and expects Tosca to accede to him. Tosca, believing Cavaradossi is saved by her agreeing to sleep with the police chief, then stabs Scarpia to death.

Thus, in the great tradition of tragic grand opera, nobody gets what he wants. The game turns against the players.

Of course, this has nothing to do with economics but does illustrate the universality of game theory. It also shows how people, seeking their own interests, often bring about their own downfall, or how a Nash Equilibrium turns out unpleasantly.

Drier contexts

Usually, however, game theory is considered within the context of drier, more practical, and occasionally grander themes, such as national and international economics, war and how to avoid it.

Peyton Young, author of "Negotiation Analysis," a book on the application of game theory published by the University of Michigan Press, offered examples of when an equilibrium is reached:

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