The Complementary Task

Formal game theory burst upon the world in 1944 with the publication of John von Neumann and Oscar Morgenstern’s Theory of Games and Economic Behavior, more than 600 pages of rigorous and abstract mathematics designed to subject various fundamental economic problems to “a treatment different from that which they have found in the literature so far.”

By 1950, it was apparent to Fortune magazine writer John McDonald that a new discipline had been organized out of what previously had been classified as strategic thought, with all the usual literary and mathematical forbears:  Machiavelli, Clausewitz, Cournot, von Stackelberg, even Ernst Zermelo, the set theorist who in the early years of the 20th century sought to build a mathematical model of the game of chess. 

With illustrations by none other than Robert Osborne (the Ralph Steadman of the 1950s), McDonald’s little book, Strategy in Poker, Business and War, probably remains the high-water mark of a certain kind of economic journalism.

But game theorists in those early days had set themselves a very difficult task. Their concepts had to be carefully prepared, like equipment to sustain a lengthy expedition.  Some enthusiasts were suffering from the technological presbyopia that often afflicts scientists and their followers — the farsighted focus on future possibilities that, for instance, caused Vannevar Bush to confidently prophesy in a national magazine the World Wide Web nearly half a century before it could be created. Besides, a lengthy territorial battle remained to be waged intellectually with technical economics.

It was in 1969 that the Royal Swedish Academy of Sciences created a new Nobel award for economics, but it wasn’t until 1994, fifty years after the appearance of Theory of Games, that the first prize for game theory was bestowed, on John Nash and two of his most fruitful elaborators, Reinhard Selten and John Harsanyi, for using von Neumann’s tools to build a secure intellectual beachhead for their field in social science.

And what exactly was it that Nash had accomplished?   On the fiftieth anniversary of his first one-page paper in 1949 (“a good time to look back at [an event], when we are still linked to it by living memories, but we have enough distance to see some of its broader historical significance”), University of Chicago professor Roger Myerson put it this way in the Journal of Economic Literature:

“A generation before Nash could have accepted a narrower definition of economics, as a specialized social science concerned with the production and allocation of material goods. With this narrower definition, Nash’s work could be seen at first as mathematical research near the boundaries of economics. But today economists can define their field more broadly, as being about the analysis of incentives in all social institutions.”  The concept of a Nash equilibrium — those situations, potentially many different ones, in which all players of a rigorously defined game are doing the best that they can, given what the others are doing  — was the unifying concept central to this transformation.

Even so, a fierce struggle had been required behind the scenes in 1994, much of it described by economic journalist Sylvia Nasar in her biography of Nash, A Beautiful Mind. Nash had succumbed to schizophrenia not long after making his seminal contribution, and only the tireless support of a loyal wife and the widening recognition of the significance of what he had achieved returned him to sufficient well-being to accept his prize. Nasar’s book became a hit movie. And Nash became the stereotype of the heroic age of game theory — brilliant, austere, and slightly daft.

Last week the Swedish Academy went a certain distance towards rewriting the history of the field.  Leave aside, for a moment, the contributions of Robert Aumann of Hebrew University, the other co-winner of this year’s prize “for analyses of conflict and cooperation.”  In honoring Thomas Schelling, the Swedes focused attention on a near-contemporary of Nash who was his opposite number in many important ways.

Literary instead of mathematical, applied instead of theoretical, humble instead of proud, engaged instead of aloof, cooperative instead of antagonistic, always on the field instead of often on the sidelines, Schelling developed independently many of the key concepts of modern game theory: credibility, commitment, the significance of promises and threats, the possibilities inherent in brinkmanship.

As the Swedish Academy’s “advanced information” puts it (that’s the technical paper accompanying the citation): “Thomas Schelling’s book The Stategy of Conflict (1960) launched his vision of game theory as a unifying framework for the social sciences. Turning attention away from zero-sum games, such as chess, where players have diametrically opposed interests, he emphasized the fact that almost all multi-person decision problems contain a mixture of common and conflicting interests, and that the interplay between the two concerns could be effectively analyzed by means of non-cooperative game theory.”

Nash and the other theorists, it was said, had set the stage. Now Schelling took on “the complementary task” of actually estimating out the equilibria for various interesting classes of games and deciding whether these had anything to say about situations occurring in the real world.  It turned out game theory had plenty of applications. “He did this against the background of the world’s first nuclear arms race and came to contribute greatly to our understanding of its implications.”

Schelling’s biography remains to be written, but the broad outlines are clear enough. He was born in 1921, the son of a Navy officer stationed in Oakland, California.  (Nash was born in in 1928, but the conclusion of World War II furnished a similar starting line to both scholars.)  Schelling entered college at the University of California at Berkley, took a couple of years off (which he spent in South America), returned, graduated in 1943 and after a little graduate work went to the US Bureau of the Budget in Washington, where he spent the rest of the war.

In 1946, he went to Harvard to get his PhD in economics. He finished his coursework and joined the Marshall Plan, which in due course evolved into the North Atlantic Treaty Organization. After five years, first in Denmark, then France and finally Washington, he took a professorship at Yale and, five years after that, in 1958, returned to Harvard, spending a sabbatical year at the Rand Corporation. (All this from Richard Swedberg’s interview in his 1990 book Economics and Sociology.) And in 1990, he moved to the University of Maryland.   

Schelling’s most influential college prof had been William Fellner, a courtly Hungarian refugee from the Nazis, deeply committed to effective public policy in the United States, who had known von Neumann in Budapest and Berlin, and who alerted his student to the problem known in those days as “fewness” — meaning those industries with only a few large companies in which strategic considerations obviously were important. At Harvard Schelling evinced a prescient interest in game theory; Wassily Leontief suggested that he first read Theory of Games. At Yale, he discussed military strategy with Albert Wohlstetter.

His most important book, The Strategy of Conflict, was written gradually in the late 1950s.  First came a chapter on bargaining — not bargaining as it had been commonly understood, over wages, say — but stripped-down bargaining, as in one of the book’s famous examples, when one truck loaded with dynamite meets another on a road too narrow for more than one to pass. From the analysis of such meeting engagements, mostly between nations, Schelling adduced the many circumstances in which cooperation could emerge, sometimes in quite unexpected ways.

A lucid discussion of this class of games, known as “chicken,” or, alternatively, “hawk/dove,” may be found on the Nobel website, along with a much-quoted line from the book:  “One cannot, without empirical evidence, deduce what understandings can be perceived in a non-zero-sum game of maneuver, any more than one can prove, by purely formal deduction, that a particular joke is bound to be funny.” In other words, the formal analysis of strategies of deterrence, commitment and coordination could go only so far.  Sooner or later — and the sooner the better — it would have to be grounded in a deeper understanding of human psychology.

(Many years later, Schelling wrote, “I have often judged that an overzealous dedication to a new methodology is helpful to its initial conquest and that the time for critical examination is after the basic theory has taken good root.”)

So what exactly had he accomplished?  He proved no theorems.  When he did attempt a formal analysis of the problem of surprise attack — what happens when you come downstairs in the night with a gun in your hand to discover that the burglar has a gun in his hand too? –“it is fair to say that his modeling did less than full justice to his intuition,” the Swedish Academy write-up delicately asserts. In time, the difficulties posed by incomplete information were cleared eventually by game theorists. But the result was that Schelling’s student Michael Spence won a share of a Nobel Prize for a formal model of signaling behavior four years ahead of his teacher.

What, then, did Schelling do? Of The Strategy of Conflict, the technical article prepared for the Swedes concludes that it “had a lasting influence on the economics profession, as well as on other social sciences.” The book and its successors, Strategy and Arms Control (co-authored with Morton Halperin in 1961) and Arms and Influence, in 1966, inspired the detailed analysis of bargaining in historical crisis situations. They played a major role in establishing “strategic studies” as an academic field.  And perhaps most important, Schelling’s works had “a profound impact” on military theorists and practitioners in the Cold War era. 

How profound?  “The secrecy surrounding military issues makes it difficult to assess the exact impact of Schelling’s work on the behavior of superpowers,” the paper states. “However a clue is that in 1993 Schelling won the US National Academy of Sciences Award for Behavioral Research Relevant to the Prevention of Nuclear War.” He served as a consultant to the US government until 1970, when he quietly resigned in the aftermath of the invasion of Cambodia.  (For a quick glimpse of the style and sensibility of Schelling’s arguments, see The Legacy of Hiroshima:  A Half-Century Without Nuclear War, a short essay he wrote in 2000.)

Nor was that all. A steady stream of novel applications of game theory to concrete problems other than those of war and peace flowed from Schelling’s pen in the years after 1960, many of them collected in Micromotives and Macrobehavior (1978) and Choice and Consequence (1984). You can see for yourself in his 20-page list of publications.  The Nobel committee singled out two particular skeins of work. 

By 1968, Schelling had become interested in patterns of racial segregation.  Finding no good discussions of individual decision-making in the literature, he began experimenting with models in which a preference for not being a minority (coupled with no very strong feelings about maintaining dominance) might suddenly “tip” neighborhoods from one racial equilibrium to another. He had a published a dynamic model in The Journal of Mathematical Sociology in 1971, and sparked the wave of interest among economists and other social scientists ultimate celebrated by journalist Malcolm Gladwell in his best-selling book The Tipping Point.

Then, in a series of articles beginning with “The Intimate Contest for Self-Command” in 1980, Schelling explored potentialities for addiction, mechanisms of self-control, the limits of devices for pre-commitment, and the implications for public policy in everything from smoking to retirement.

In recent years, Schelling has worked mostly on problems of global warming, offering the Marshall Plan as a good model — perhaps the only model, he says  — of a means of sharing obligations to reduce greenhouse gases around the world.  It is yet another deeply-grounded insight into the immensely complicated problem of how to share collective assets and liabilities among of world of game-playing nations.

By pairing Schelling’s recognition with that of Robert Aumann, the Swedes have offered a powerful object lesson, to insiders and outsiders alike, about the different paths by which economics may proceed. Aumann, 75, is a mathematician by training. Having fled the Nazis, his family settled in New York. Aumann received a PhD at the Massachusetts Institute of Technology (where he knew John Nash), then emigrated to Israel, where he has lived ever since in Jerusalem. A son died in combat in 1982.

Working deep in the community of game theorists, Aumann carefully thoughy through the details of some of the concepts that Schelling treated less formally — the interactions that can lead to long-term cooperation, in particular. Ariel Rubinstein, a game theorist of the next generation, describes Aumann as an academic paragon, interested in the pure logic of strategic thought, with almost no concern for its immediate usefulness — and yet a prime mover behind the creation of Hebrew University’s Center for Rationality, an institute for economists, psychologists, computers scientists, lawyers, mathematicians and philosophers that is among the leading social science research centers in the world.

Indeed, the joint award calls to mind a celebrated series of distinctions made by Donald Stokes, longtime dean of Princeton’s Woodrow Wilson School of Public and International Affairs.  Stokes assigned the motives behind scientific research to a simple matrix.  In one quadrant was work inspired by the quest for fundamental understanding but with little consideration for usefulness:  this was pure basic research, as exemplified in physics by Niels Bohr. In another quadrant was work whose practical value was all that mattered, with no concern for abstract knowledge:  this was pure applied research, as exemplified by the stream of inventions emanating from Thomas Edison’s “invention factory.”

In the third quadrant, equally motivated by an interest in fundamental understanding and a concern for its usefulness, was where the payoff was likely to be greatest:  this was the quadrant of Louis Pasteur, the father of germ theory, equally committed to understand and to control the microbiological processes he discovered, thereby saving millions of lives. (The fourth quadrant, work undertaken with no concern for use or understanding, was naturally empty.)

Like the other really controversial choice in the short history of the prize for economics — the decision in the committee’s fourth year to cite Sir John Hicks and Kenneth Arrow jointly instead of honoring Arrow alone and finding some other way to recognize Hicks’ early but less-important contributions — the groupings of the laureates in the first two prizes in game theory will be debated as long as there are economists, game theorists, mathematicians and civilians to debate. Always the prize-givers must take various social considerations into account. After fifty years, historians may choose to rearrange the laureates if they like — journalists even sooner than that.

For in many ways, John Nash and Thomas Schelling make a better pair, while John Harsanyi, Reinhard Selten and Robert Aumann form a neater package to explain. By recognizing the 84-year-old Schelling while he is still vigorous, by acknowledging the existence the Pasteur quadrant in economics, the complementary task, the Swedes have performed a memorable service.