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GAME theory is back in the limelight. Two of its long-time proponents have been awarded the Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel for 2005. Thomas C. Schelling, a retired Professor in the Department of Economics and School of Public Policy at the University of Maryland, and Robert J. Aumann of the Centre for Rationality at the Hebrew University of Jerusalem will receive the prize later this year. On October 10, the Royal Swedish Academy of Sciences announced that the two academics were being honoured "for having enhanced our understanding of conflict and cooperation through game theory analysis".
The last time game theory practitioners won a Nobel was in 1994, when John Nash Jr. shared the prize with fellow American John Harsanyi and German academic Reinhard Selten. Game theory - the analysis of how strategic choices are made - gained popularity after the story of Nash's life was portrayed by Russell Crowe in the 2001 Academy Award-winning film A Beautiful Mind, which was based on a book of the same name.
The theory of games is certainly not trivial, either in terms of the techniques employed or in the range of subjects addressed. In order to explain and predict the interaction and behaviour of social agents (governments, individuals, institutions, firms and so on) game theory exponents typically employ complex mathematical models. These models are often quite simplified abstractions of real-world interactions but are supposed to offer a tractable way of predicting likely outcomes among the participants in a "game". However, the games that game theorists play can be quite deadly. Significantly, all five Nobel Prize-winning practitioners of game theory in economics since 1994, including the two for 2005, have at some time or the other worked on developing strategies for the United States military establishment.
The most commonly cited example of games is the prisoner's dilemma, variations of which are frequently shown in films and television serials. Two partners in crime are lodged in separate rooms at the police station and offered a similar deal. If one squeals on the other, he can escape punishment while the other receives a life in prison. If neither implicates the other, both are given moderate sentences, and if both implicate the other, the sentences for both could turn out to be severe. Each player has a "dominant strategy" of implicating the other, and thus in equilibrium each receives a harsh punishment. However, both would be better off if they remained silent. In a repeated or iterated prisoner's dilemma, cooperation may be sustained through "trigger" strategies. Practitioners of game theory draw lessons of strategic behaviour from everyday games such as bluffing in poker, and apply them to much more frightening circumstances such as, for instance, how to wage war. (Bluffing, in this case, is treated as being similar to nations posturing about their military might.)
Although game theory adherents point to elements in the Talmud and Sun Tsu's writings as being suggestive of early notions of game theory, the modern edifice for game theory was built on the work of John von Neumann and Oskar Morgenstern who, in 1944, published Theory of Games and Economic Behaviour. Game theory is regarded more as a tool than as a unified body of theory that can be readily used to explain happenings in real-life situations. In order to apply game theory (in economic modelling, for instance), stringent assumptions are often necessary. Indeed, game theory advocates accept that there is a constant trade-off between realism and the solvability of a problem. They claim that in the realm of economics their method has been useful in the study of antitrust policy, auctions (of radio spectrum licences to mobile phone companies in the U.S., for instance), in trade negotiations, to study how firms compete and collude with others, or what strategies individuals or communities would/should adopt when competing for scarce resources.
Jorgen Weibull, Chairman of the prize committee, said that game theory is relevant because it "helps explain economic conflicts like price competition and trade wars". "I think the main impact is on economics, but it also applies to other social sciences," he said. Aumann (75) and Schelling (84), who have never worked together, were cited by the Academy for helping explain "economic conflicts such as price wars and trade wars, as well as why some communities are more successful than others in managing common-pool resources". The pair's work could be applied to understand how merchant guilds, international trade treaties and even organised crime rings develop and operate.
THE evolution of game theory from the 1950s represents a classic case of how "pure theory" in the academic world is closely aligned to the U.S. military-industrial complex. Harold Kuhn, a mathematician from Princeton who chaired the Nobel seminar dedicated to Nash in 1994, pointed out that "it is a historical fact that initially the main financial support in this area (game theory) came from military agencies in the United States" (the proceedings of the seminar can be accessed at http://nobelprize.org/economics/laureates/1994/nash-lecture.html). In fact, Aumann observed in The New Palgrave Dictionary of Economics (1987) that the major applications of game theory were "to tactical military problems", involving missile deployments, fighter-fighter duels and other issues relating to purely military tactics and strategies. "Later," Aumann observed, "the emphasis shifted to deterrence and Cold War strategy with contributions by political scientists like Herman Kahn, (Henry) Kissinger and Schelling." Kahn was a nuclear strategist who later turned to "futurology". Like many of the leading game theorists during the 1950s and 1960s, Kahn joined the Rand Corporation where he worked on military strategy. Unlike many other scholars and strategists, he believed that a nuclear war could be won. At Rand, he studied the application of such analytical techniques as game theory and systems analysis to military theory. Aumann points out that the Rand, funded by the U.S. Air Force, "was for many years the major centre for game-theoretic centric research". Kuhn pointed out that he had hired John Harsanyi and Reinhard Selten (Economics Nobel winners in 1994) as consultants to a project he initiated for a research company in Princeton, Mathematica (not to be confused with a computer programme of the same name). Kuhn said that the project was funded by the Arms Control and Disarmament Agency.
In a long interview given to his colleague Sergui Hart at the Hebrew University in January 2005, Aumann said that his first assignment in game theory was on problems relating to the defence of a city against a squadron of aircraft carrying nuclear weapons, some of which were decoys. The project was sponsored by Bell Labs, which, according to Aumann, was "developing a defensive missile" (The text of the interview can be accessed at http://www.ma.huji.ac.il/{tilde}hart/papers/md-aumann.pdf). Aumann said that in 1961 Kissinger spoke at an international conference on game theory, about the "game-centric thinking" in Cold War diplomacy and international relations. He also pointed out that President John F. Kennedy "was influenced" by such theories.
In fact, Aumann points out that at the height of the `Red Scare' in the late 1950s and early 1960s, there was apprehension among strategic analysts that the building of nuclear fallout shelters in the U.S. could be interpreted by the Soviets "as extremely aggressive behaviour". Aumann said: "Why should you build shelters? Because you are afraid of a nuclear attack. Why are you afraid of a nuclear attack? Well, one good reason to be afraid is that if you are going to attack the other side, then you will be concerned about retaliation." The problems that the early proponents of game theory dealt with were almost exclusively concentrated on the strategies relating to the deployment of the U.S. war machine. It is obvious that state support and direction played a key role in shaping the agenda of game theorists until the end of the Cold War.
IRONICALLY, Schelling's most influential works are far-removed from the realm of economics. They relate much more to how and under what conditions American military might ought to be deployed. His most important contribution to this effort was in 1960, when he published The Strategy of Conflict. It focussed on how the U.S. and the Soviet Union maintained credible nuclear threats, which according to him were unlikely to be actually used, given the possibility of mutual annihilation. According to Wikipedia, this work "is considered one of the hundred books that have been most influential in the West since 1945". He extended his exposition on the theories of warfare in "Arms and Influence", which was published in 1966.
The Royal Swedish Academy of Sciences said Schelling's work "had a profound impact on military theorists and practitioners in the Cold War era, played a major role in establishing `strategic studies' as an academic field of study and may well have contributed significantly to deterrence and disarmament among the superpowers".
However, sceptics have noted that Schelling's theories, couched as elegant academics, played a highly destructive role at the height of the U.S. attack on Vietnam in the 1960s. Fred Kaplan, who wrote a piece in slate.com on the day the prize was announced, pointed out that Schelling had played an important role "in formulating the strategies of `controlled escalation' and `punitive bombing' that plunged our country into the war in Vietnam". "This dark side of Tom Schelling, he wrote, "is also the dark side of social science - the brash assumption that neat theories not only reflect the real world but can change it as well, and in ways that can be precisely measured."
Schelling's work of 1960 applied game theory principles in the realm of bargaining to the practice of war. His experience as a trade negotiator during the 1940s may have influenced him in adopting this apparently sanitised approach to the business of killing. In his book, he observed that there were "enlightening similarities" between manoeuvring in a "limited war" and in a traffic jam, or in deterring Russia or one's children.
Kaplan points out that in the 1950s, the "key dilemma" in the U.S. establishment led by President Dwight Eisenhower was the "emerging nuclear parity between the United States and the Soviet Union". The U.S. position relied on a policy of "massive retaliation" through a nuclear strike if the Soviets invaded Western Europe. But if the Soviets also retaliated similarly, this policy would no longer be effective. What should the U.S. do in such a situation?
Schelling's answer was to retaliate "in a punitive sense" through "limited or graduated reprisals", aimed at inflicting "civilian pain and the threat of more". In Arms and Influence, he elaborated on the theme. "The power to hurt," he wrote, "can be counted among the most impressive attributes of military power.... To inflict suffering gains nothing and saves nothing directly; it can only make people behave to avoid it." "War," he noted, "is always a bargaining process." War, he argued, must be waged in a way that would maximise "the bargaining power that comes from the capacity to hurt... [and cause] sheer pain and damage." These, he pointed out, were "the primary instruments of coercive warfare".
Schelling's concepts were used by the U.S. administration led by Lyndon Johnson in 1964 when it escalated the military involvement in Vietnam. In fact, Schelling was intimately connected through a close friend, John McNaughton, who, as Assistant Secretary of Defence, reported to Robert McNamara, then Secretary of Defence. Kaplan points out that Schelling's "lessons" are recognisable in the classified memorandums reproduced in The Pentagon Papers, the secret history of the Vietnam War that Daniel Ellsberg leaked to The New York Times.
The "theory" used aimed at deterring the Communists in North Vietnam from extending the war to the South. This was to be done by mounting "carefully graduated military force". The idea was to deploy troops "on a very large scale, from the beginning, so as to maximise their deterrent impact and their menace. A pound of threat is worth an ounce of action - as long as we are not bluffing".
In 1971, Schelling published a widely cited article dealing with racial dynamics called "Dynamic Models of Segregation". In this paper, he showed that a small preference for one's neighbours to be of the same colour could lead to total segregation. Prejudice in group preferences, he claimed, can take on a "self-sustaining momentum".
Schelling is among those who believe that the seriousness of the problem of global warming is overstated. Drawing on his experience during the implementation of the post-war Marshall Plan, he has argued that the issue of global warming is fundamentally a bargaining problem. He has pointed out that if the world is at all able to reduce emissions, poor countries will receive most of the benefits while the rich countries will bear most of the costs. Critics would say that this unsympathetic treatment of developing countries' plight is largely because his view fails to take into account the fact that advanced countries have contributed significantly more to the problem of global warming through emissions of greenhouse gases in the past, which impose a cost in the present and in the future.
Aumann's work is in sharp contrast to that of Schelling. Holding dual citizenships of the U.S. and Israel, he is a mathematician who regards game theory as applied mathematics. Born in Germany, he migrated to the U.S. in 1938, days before the Kristallnacht riots (the night of the broken glass), which marked the launch of a pogrom against Jews in Austria and Germany. He obtained a doctorate in mathematics in 1955 from the Massachusetts Institute of Technology. In 1956, he joined the Mathematics faculty of the Hebrew University of Jerusalem. His main contribution has been in the area of repeated games, which are situations in which players encounter the same situation over and over again.
Aumann, by admission a devout Jew, is a member in the Professors for a Strong Israel (PSI). The PSI unites academics who share a concern for Israel's security and the preservation of its Jewish character, and supports the principle of a Greater Israel.
In his reaction to the announcement of his winning the Nobel Prize, Schelling told National Public Radio (NPR) on October 10 that he did not consider himself as a game theorist, only a consumer of game theory. Robert Aumann, he said, "is a genuine game theorist".
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