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17 November 2000

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Ariel Rubinstein

Garbage disposal and the nuclear arms race

By Ariel Rubinstein (translated from Hebrew by HAARETZ).
Ariel Rubinstein is a professor of economics at Tel Aviv and Princeton universities. He specializes in game theory.

Here is a commentary on "Prisoner’s Dilemma: John von Neumann, Game Theory and the Puzzle of the Bomb" by William Poundstone,translated into Hebrew by Nili Landsberger. Zmora Bitan, 368 pages, NIS 78.

In a certain front yard of a certain apartment building (or perhaps in every yard and every building), there is a garbage bin. With an increase in the number of residents who fail to seal their garbage bags properly, the stench will also increase - to the extreme pleasure of the flies and mosquitoes and the utter dismay of the other residents. Why don’t they seal their bags of trash? Because when the rational apartment dweller comes downstairs, holding the average, slightly ripped garbage bag, he reasons that the slight improvement he could make to the world’s olfactory situation if he took the trouble to go back upstairs and place the torn bag into one without any holes simply does not justify the effort involved.At this point in time, our rational neighbor will choose the action that suits him best, in keeping with his own preferences and priorities, which are a combination of his wish to minimize his own personal inconvenience and the world’s stench level. Or as game theorists (and economists) might say, our neighbor is simply being a "rational person."

In our story, each of the residents is rational, and the stench rises all the way to the top floor. There isn’t a great deal of love lost between the neighbors, but in the discussion held by the residents in the lobby of the apartment building, everyone nods in assent when someone says that something has to be done. After all, we’re talking about "everyone’s garbage can." Every resident understands that if only everyone there made "just the slightest effort," then everyone would be so much better off.

"It’s a dilemma of society that needs to be resolved," says the building’s "sociologist." Another neighbor, known as the "pedagogue," proposes initiating an information campaign among the residents, to help them embrace the idea of a general good that would benefit the others. The "strategist" suggests that starting next Sunday, a new system of understandings will take effect. Everyone will be especially careful with their garbage bags, and if any of the residents are found to be derelict in their duties, the state of anarchy will resume.

This agreement should persuade the rational neighbor to be especially cautious, since hanging in the balance is not only the minor effect he might have on the current olfactory situation, but also the entire housing situation for years to come. Someone else proposes breaking the bones of anyone caught red-handed, thereby ensuring that no one would even consider being careless. That’s how it is in this apartment building, which is a "gentle weave of contrasts." In the end, there is no moral to be drawn.

The book describes another scenario in vivid detail: It is the 1950s, the arms race is at its height, and people are terrified of an imminent nuclear holocaust. In September 1949, the United States reveals that the Soviets also have the bomb. Everyone understands that as nuclear weapons proliferate, there will be a greater probability of a nuclear holocaust brought on by accident, by the whim of a despot, or simply because the scientists did not correctly calculate what happens when warheads begin to degrade. In the capitals of the superpowers, "top secret" memos are being written, recommending that nuclear arms procurement be speeded up. "If we are the only ones to develop a neutron bomb," say the memos, "we will achieve an immense strategic advantage. Even more so if our rivals (who cannot be trusted) is also developing the bomb, so that we can at least prevent them from gaining a strategic advantage."

Each summer, the RAND Corporation in Santa Monica, California would convene a team of the "best and the brightest minds in the land." This brain trust was asked "to think the unthinkable," and along with planning for life in the wake of a nuclear attack, it was asked to advise the United States government on nuclear strategy. Several members of the group were involved in the development of game theory, based on the publication of "Theory of Games and Economic Behavior" by the eminent mathematician John von Neumann and the economist Oskar Morgenstern. There is no denying that members of the group were brilliant, and aware that the future of the world rested on their shoulders. They knew that if nothing changed, and each superpower was allowed to adopt a "rationalist" strategy (in other words, nuclear arms proliferation), the world would be dragged to the brink of the abyss.

We do not know exactly what was said at the RAND Corporation. I would not be surprised if there were some who took the pedagogic approach, proposing that the finest men of letters in the world embark on a propaganda campaign that would put pressure on the leaders (especially those of the "others") to end the arms race. We know that there were those at RAND who believed the arms race could be stopped by reaching understandings between the superpowers, so that if any side advanced in the arms race, the other would match it. There were also some who felt that if the Soviets got ahead in the arms race, the West ought to bomb them before they could bomb the West. And then there was yet another voice that argued that there was no reason to wait - that nuclear attack should commence immediately, with the goal of establishing a global government that would enforce a new world order. That same person said: "If you say: ’Why not bomb them tomorrow?’ I say: ’Why not today?’ If you say: ’Today at five o’clock,’ I say: ’Why not at one o’clock?’"

This glib spokesman did not live in an apartment building, but on the lawns of Princeton. He was a widely admired man who lived in the myths that surrounded him, a person who could easily divide eight-digit numbers and commit dozens of history books to memory; a man who made critical contributions to most areas of mathematics, who was considered a father of the digital computer, who was known as "the most brilliant mind in the world" (Einstein was still alive at the time), a Hungarian Jew who converted (not all that relevant to this essay, but why not mention it?) - John von Neumann, the hero of this book.

At this point, the reader may be wondering about the connection between the two stories, asking what any of this has to do with "the prisoner’s dilemma" and with game theory. Game theorists are aware that the two stories are not identical, but they find a common denominator: If each participant behaves in a rational manner, he will also be thinking about what the other participants are thinking and doing, and he will opt for the same course of action (i.e., he will be sloppy when throwing out the garbage, or will accelerate the arms race). However, the consequences of these rational moves are worse for all participants than they would have been if each had behaved in an irrational manner (taking care to dispose of garbage bags properly and avoiding an arms race).

In game theory, such a situation is called "the prisoner’s dilemma," after a hackneyed story in which two men are arrested and held in two separate cells, and each one has to decide if he is willing to turn state’s evidence against the other. Game theory identifies and analyzes sets of considerations in situations where rational beings interact.

Some books spark young people’s interest in scientific themes. This is the case, for instance, of Simon Singh’s "Fermat’s Enigma," which interposes anecdotes from the lives of mathematicians with superb math problems that underscore the true nature of mathematics. I would not be surprised if, in another 20 years, several young people of our generation professed that their love for mathematics was born of an incredible childhood experience - their reading of "Fermat’s Last Theorem."

William Poundstone’s "The Prisoner’s Dilemma" is not such a book. There are books that contain an important human message; an example is Sylvia Nasar’s "A Beautiful Mind: A Biography of John Forbes Nash," about the man who received a Nobel Prize for Economics for his fundamental contributions to game theory. The life story of von Neumann is not as fascinating as that of Nash, and the book by no means offers any important messages to humankind. Nevertheless, this is an interesting book, at times even mesmerizing. It is a stubborn attempt to present game theory in an erudite and popular fashion, while taking up an arcane historic topic (the determination of nuclear strategy in the 1950s), in which game theory ostensibly played a part. But Poundstone falls into the unavoidable pitfall that game theory sets for those who take an interest in it from the outside, and perhaps even those who engage in it from within. The quintessence of game theory, its objectives, and the relationship between it and reality, are unclear not only to Poundstone, but even to those who have engaged in game theory. The author’s inherent confusion between theory and reality, between description and prediction, between usefulness and abstractness, is the necessary result of the confusion that exists in game theory, economics and perhaps in every social science.

Poundstone claims that "The prisoner’s dilemma is one of the great ideas of the 20th century. It is simple enough to be understood by everyone, but nevertheless it retains its basic significance." The prisoner’s dilemma is a simple idea that makes use of good stories, but its ability to be understood does not necessarily make it into such a great idea. Poundstone speaks of a "solution" to the prisoners’ dilemma as if we were speaking of some riddle waiting to be solved. At the same time, he is aware that "most theoreticians of game theory believe today that the prisoner’s dilemma will never be solved," and that "game theory has become a sort of strategic oracle ... but as with every oracle, the problem is that the answers of game theory depend on how the questions are posed.

Poundstone uses matrixes to demonstrate "games." He writes: "The prisoner’s dilemma is much more than a mere story, it is a precise mathematical structure as well as a problem in everyday life." The graphic representation of these problems in matrix form is convenient for the experienced user, and important for analytical use. But for the readers of this book, it is nothing but a misleading illusion of "scientific method and exactitude."

The author explains game theory as a system of "recommendations," and frequently relates to it by saying things like "the theory says." But he too understands that it is but a compendium of concepts, models and formal arguments, not a guide to a happy life. Poundstone often employs the familiar rhetoric of the academic world. He speaks of "the far-ranging implications (of game theory) on policies, on social norms" but has a hard time providing any examples of said implications.

Poundstone would have the reader believe that von Neumann used game theory to formulate his recommendations on preemptive nuclear war. But the author has not the slightest idea what cognitive moves led von Neumann to reach his conclusion. At one point, he even quotes the mathematician Paul Halmos, who said: "Von Neumann’s support of the preemptive war derives from the great animosity he has for Communism, due to his childhood memories of the Kun government in Hungary after World War I."

One final message: The following statement is controversial, and expresses my own views on game theory and its utility. As I see it, game theory is a fascinating and abstract discussion that is closer to philosophy than to the economics pages of the newspaper. It has no direct applications, and if it has any "practical utility" (which I doubt), then it is in the winding and inscrutable way that our minds absorb ideas and use them when the time comes for real action. And this too must be proved.

Garbage disposal in an apartment building and the nuclear arms race may have a similar strategic structure, just as the problems of two prisoners in individual cells are similar to those of the CEOs of two major banks who are competing for an emerging market. One may conclude that there is utility in the abstract discussion of game theory, which covers all situations that may fall under the heading of "the prisoners’ dilemma." But one could also reach a different conclusion: The rational person in the apartment building has a pretty fair understanding of his building’s problems and therefore also a pretty fair understanding of the problems of the world. Meaning, for instance, that it is far from obvious why Israel’s nuclear policy might be any better if the relevant discussions were held in the lounges of post-graduate schools of government by graduates of courses in game theory, than in the lobbies of apartment buildings, with the participation of the public at large.

The book misses the psychological-sociological story underlying game theory. It turns out that even "rational and educated" people feel a need to turn to "authorities" without having any good reason to believe in what they will be told. Game theory is not a conspiracy of the American defense establishment (as has been alleged by some). However, I am greatly perturbed by the question of whether, in actuality, it serves the needs of the social and academic elite, by removing the important questions from the popular civil agenda and entrusting them to the closed world of the privileged few, the magicians who ostensibly hold the keys to the secret language of science. > Les Textes > English Texts > Authors - Site powered by SPIP