Tuesday, October 10, 2006

Game Theory is Everywhere!

Until this week, I hadn't really thought about Game Theory since I took a college course in the philosophy of mathematics, cheesily titled "Excursions in Mathematics" (who comes up with these titles, anyway?). But first, in the discussion mentioned here earlier (I've finally made my exit, convinced that there simply is not enough charity in the world for opposing views to meet constructively in such an artificial social environment), Game Theory was used as a weapon against me, presumably because, as a Christian, I would have never studied it before.

And now, this: I just wanted to read about football, so I went to ESPN.com's Tuesday Morning Quarterback, a weekly column which reviews Sunday and Monday's NFL games. However, author Gregg Easterman had other plans. In the middle of a series of observations about football, he wrote

When Researchers Projected Magnetic Fields Into Dick Cheney's Brain, He Became Friendly: Economists call it the Ultimate Game, and have long contended it proves Homo sapiens insufficiently logical. Here's the situation. Two strangers are brought together by a third person who holds $1,000. He tells them the money is theirs to divide on these terms: Stranger A must propose how to split the $1,000, and Stranger B must either accept or reject A's offer. That concludes the game, no second round. Classical economists maintain Stranger A should say, "I propose that I get $999 and you get $1," and Stranger B should immediately respond, "I accept." Pure economic theory says A should maximize his gain by shafting B out of every possible farthing, while B should calculate that since his sole choice is between $1 and nothing, $1 is better. Yet researchers have played this game with volunteers in many nations, and it never works the way theory says. The bare-minimum offer is always rejected. Generally, A must offer at least 30 percent or B says no and both players get nothing. Classical economists have long harrumphed that B's response when the game is played with real money shows human beings are too emotional and insufficiently focused on maximizing outcomes.

This pot was stirred last week when researchers led by Dario Knoch of the University of Zurich reported that using magnets to disrupt the right prefrontal cortex of volunteers playing Stranger B caused them to become much more willing to accept low offers. Now, if someone was using magnetic waves to scramble parts of your brain, your bargaining skills might decline, too. ("Herr Professor Doktor, ve haff discovered zat when ve knock der volunteers unconscious mit ein sledgehammer, zey refuse to aufgeparticipatehaffen* in the experiment.") But I think tests like the University of Zurich study only point to the Ultimate Game being so flawed that it mainly shows us faults of classical economics.

First, the game assumes money is superior to all other forms of possessions, including psychological well-being. But the world doesn't work that way. If I am Stranger B and accept the $1 offer, I have a dollar bill but also feel like a total dupe: And how can being made to feel like a dupe be worth a mere dollar? Any small-percentage offer accepted by B would make B feel unhappy and taken advantage of, while rejecting the small-percentage offer gives B the pleasure of feeling retribution was achieved against A. Once the offer gets up to around 30 percent, then the value of the money might equal whatever unpleasant thoughts B will experience when seeing A cackling and counting a larger pile of loot. Reactions like rejecting very low offers do not, as classical economists maintain, show that B fails to understand economics. They show that B understands money is not everything!

Next, people in the B role might derive long-term benefits from refusing low offers, and these benefits might exceed the value of the money forgone. In his important new book "The Origin of Wealth," Eric Beinhocker speculates that the kind of circumstances in which B refuses a too-low offer are "the cornerstone for social cooperation that is essential for wealth creation." In order for the free market to serve the overall welfare of society, Beinhocker maintains, all must mutually agree not to participate in arrangements that exploit those with weak bargaining positions. Society must be structured such that A would feel ashamed of offering only $1 to B, and would offer a fair sum in order to feel good about the transaction. If parties in strong positions offer fair sums, the result is mutually beneficial trading for everyone, including the strong. (Are you listening, Wal-Mart?) "The Origin of Wealth" is a major new book that ought to be commanding significant attention. Beinhocker, a management consultant for McKinsey & Company, argues persuasively that market economics is not a war of all against all. Market economies do best, Beinhocker says, and the welfare of society rises most, when people voluntarily take each other's interests into account.

Finally, TMQ contends economists misunderstand their own Ultimate Game because the focus of discussion is always on what Stranger B will accept. The key to this puzzle is not B but Stranger A -- who is a total, utter idiot for offering only $1 because this insures A gets nothing! Offers in which A seeks to claim the lion's share are irrational on A's part, because such offers will fail. I would argue there is only one wise offer for A to make: that they each get $500. A 50/50 split is sure to be accepted, thus insuring Stranger A of pocketing $500. A fair-minded person playing the A role would offer a 50/50 split because it is fair; economically this is also the logical move, because it guarantees a successful transaction. By focusing on whether B will accept an inequitable offer, economists skip over how dumb it is for A to make such an offer. By contrast, fairness leads to benefits for both parties, which is the big point of "The Origin of Wealth."

(*Note: Tuesday Morning Quarterback has long contended that any verb can be converted into pseudo-German using the formula aufgeXXXXXhaffen. Thus to jog becomes to aufgejoggenhaffen, etc.)


Did anyone expect such lucid thoughts from a football writer?!?

1 comment:

Brian Cubbage said...

Certain disciplines in the social sciences are dominated by game-theoretic thinking, and I agree with the present author that there are inherent limitations to its usefulness, both as a heuristic device and as an explanatory framework. In political science, for instance, the parallel to the maximizing assumptions of economics is "rational choice" theory, which stipulates that political actors always act in such a way as to maximize the realization of their interests.

A professor of mine in graduate school told a story of a political science seminar he had taken at his graduate school. The graduate program there attracted a large proportion of students from all over the world. One of the students, an Eastern European, was routinely annoyed by the tendency of his fellow students to introduce anecdotal evidence by prefacing it with the words "In my country...". However, one day, the student just couldn't resist doing it himself. During a disquisition on rational choice theory, the student brusquely interrupted and said, "In my country, the labor unions support the monarchy. Explain THAT with your rational choice theory!"