Roanoke Times
Copyright (c) 1995, Landmark Communications, Inc.
DATE: SUNDAY, February 19, 1995 TAG: 9502180032
SECTION: EDITORIAL PAGE: G3 EDITION: METRO
SOURCE: ALAN SORENSEN EDITORIAL PAGE EDITOR
DATELINE: LENGTH: Long
My mother, who believes in activity with a purpose, did not approve. In a court of reasonableness, I'm sure, we could not have defended our obsession. We played anyway.
The reigning champion we called Mr. Universe. It was mostly a joke, but we coveted the title. Each of us strived mightily to win; what, otherwise, would be the point of playing?
But of course, the suspense over who'd be the next Mr. Universe mattered to no one else. It doesn't matter now.
Our games offered diversion, an exercise for memory and strategy, an outlet for a male kind of rivalrous camaraderie. But to an outsider not engaged in the playing, it must have seemed a trivial pursuit that stretched idleness and interfered with sleep.
I was reminded of this passion by a book I've just finished with a forbidding title: "Prisoner's Dilemma: John Von Neumann, Game Theory, and the Puzzle of the Bomb." It describes how games can become consuming and irrational.
A friend had lent the book to me, but I didn't start reading it until newspaper colleagues brought to my attention the amazing story of John Nash.
A Princeton mathematician with ties to West Virginia and family in Roanoke, Nash recently won a shared Nobel Prize in economics even though he had suffered for decades from schizophrenia. As a student of Von Neumann (a Hungarian emigre credited with helping to invent game theory, computers and nuclear weapons), Nash figures in the "Prisoner's Dilemma" because he helped develop important precepts of game theory.
Now, don't imagine I know anything about math. This book was written for laymen; I can barely figure a restaurant bill. But, as I understand it, a "Nash equilibrium" is a solution to a conflict in which each player is satisfied that he adopted the most rational strategy, given the other players' strategies and the rules of the game.
The strange thing that Nash and others discovered is that this "equilibrium" outcome is sometimes illogical. Game theory proves, in other words, that individuals rationally maximizing their own advantage can produce a collective result that is anything but rational.
Consider the prisoner's dilemma. Two members of a criminal gang are arrested and held in isolation from each other. Police lack sufficient evidence to convict the pair on the major offense, so they plan to sentence both to a year in prison on a lesser charge. But to each prisoner they offer a Faustian bargain: Testify against your partner, and you'll go free while he gets three years on the principal charge. The catch is: If both prisoners testify against each other, both will be sentenced to two years in jail.
Assuming your only concern is with minimizing your own sentence, what do you do? You know the other guy is being offered the same deal. If he refuses to testify against you, but you testify against him, you get off scot-free, sparing yourself a year in jail. If he rats on you, and you also testify against him, you'll get two years - but you would have gotten three if you didn't testify.
The fact is, you're better off testifying in either case. No matter what the other guy does, your agreeing to rat on him takes a year off your sentence.
Hence the dilemma. Your partner, assuming he's equally rational, will come to the same conclusion: He'll testify against you. It's the Nash equilibrium. Each of you has done the rational thing, given what the other player did. But you'll both end up spending two years in the pen whereas, if neither had agreed to testify, each of you would have gotten just one year.
I don't think this dilemma is a mere abstraction divorced from reality. As the book's author, William Poundstone, points out: "The [dilemma's] main ingredient is a temptation to better one's own interests in a way that would be ruinous if everyone did it. That ingredient, regrettably, is in ample supply."
There are other situations in which individually rational strategies produce collectively irrational results. One of my favorites cited in the book is the "dollar auction."
Announce to a crowd that you will auction off a dollar bill. You'll give it to the highest bidder, but with a twist: The second-highest bidder also has to pay the amount of his last bid, and gets nothing in return.
Would you bid 1 cent for a dollar? Of course. Well, how about 2 cents? Why not? But then the person who bid 1 cent has an interest in bidding 3; otherwise, he loses his penny. And so on.
When the bidding gets to a dollar, it really gets interesting. At that point, the person who bid 99 cents has an interest in bidding $1.01. (His choice is between losing 1 cent and losing 99 cents.) Once the bid goes to $1.01, then the dollar-bidder has an interest in bidding $1.02. And so on, up and up until the auctioneer makes out like a bandit.
It's crazy. But anyone who has thrown good money after bad, or kept to an increasingly painful course because too much was "invested" to quit, will appreciate the resonance with real life. The paper first describing this auction, by Rand Corp. researcher Martin Shubik, was published in 1971 - at the height of the Vietnam War.
Indeed, as Poundstone points out, it's no coincidence that prisoner's-dilemma theory emerged during a nuclear arms race. For America and the Soviets, the preferred outcome would have been to possess a hydrogen bomb without the other side having one. (The prisoner rats on his partner, gets off entirely.) The worst outcome would be to lack the H-bomb if the other side had it. (The sucker doesn't testify while his partner does.) To avoid the risk of the other side defecting, the option of neither side building a bomb (neither prisoner testifying) was unthinkable. Both nations had little to gain if both developed the bomb at great expense and danger to each other and to the world. But that outcome, rational for each nation, irrational collectively, is what happened.
I'm sure the prisoner's dilemma will continue to confound us in everything from baseball strikes to efforts at regional cooperation, unless we figure out ways to assume the risk of cooperating for the common good, trusting others to do likewise.
Many years ago, a Mr. Universe of sorts recommended just this solution to the dilemma when he urged us to "do to others as you would have them do to you."
by CNB