A Snowball Flung on the Uppermost Slopes

As it happened, the Market Design Working Group was holding its regular meeting at the National Bureau of Economic Research this weekend.  So, three days after his Nobel prize was announced, Alvin Roth, 60, who is in the process of moving to Stanford University from Harvard, returned to Cambridge, Massachusetts.  He dined with his children, taught his old class Friday morning and spent the rest of the day hanging out at the workshop he founded to discuss the work for which he is best known – the vastly expanded system of kidney exchange.

Meanwhile, Lloyd Shapley, 89, in Pacific Palisades, apparently scrupled for a couple of days behind the scenes before friends persuaded him to accept. Only then did the reclusive legend put on a clean shirt and a wan but happy smile and, on Monday morning, in the artfully-staged presence of an Associated Press photographer, greet the world. (Well-documented similar pains were take many years ago with John Nash.) Here’s a somewhat sanitized UCLA account. You have to admire the ingenuity of the committee that framed the prize.

Roth can take care of himself.  Supremely personable, somehow a grand old man at 60, he is surrounded by generations of students and researchers, some of them computer scientists, working on all kinds of cutting-edge topics.  These include circuit breakers (forced trading halts) in panicked markets, random assignments in long waiting lines, school choice, new wrinkles in the auction of broadcast spectrum rights, corporate restructuring refinements and all manner of other market processes, anything, in other words, that might be improved by a little engineering.  NBER president James Poterba told the assembled throng, “I spend more time than most talking about why government should spend money on fundamental research, and this is about the easiest case there is to make.”

Shapley, on the other hand, requires some explaining.  Robert Aumann, the Israeli mathematician (and a historian of game theory) who shared the 2005 prize with Thomas Schelling, has called Shapley the greatest mathematical game theorist of all, including, presumably, vastly better-known John Nash and even John von Neumann. Martin Shubik, of Yale University, who pressed Shapley’s nomination harder than anyone else, agreed, noting that others, including Sidney Siegel, Thomas Schelling and Daniel Kahneman, had also contributed much to the analysis of strategic behavior.

The junction between Shapley and Roth is a 1962 paper that Shapley wrote, with David Gale, called “College Admissions and the Stability of Marriage,” published in American Mathematical Monthly. Though it contains little mathematics formal notation, the article rendered precise  an approach now known as the Deferred Acceptance Algorithm. (Gale died, at 86, in 2008.) Twelve years later, in “The Core and Indivisibility,” Shapley and Herbert Scarf, of Yale University, extended the analysis to analyzed traditional “one-sided” markets for indivisible (or lumpy) goods, in which preferences matter only one way – to buyers of houses, for instance; or kidney recipients (like houses, kidneys have no preferences for their owners).

Roth, who graduated from Columbia University in 1971 and has a 1974 PhD in operations research, from Stanford, recognized the relevance of their proof to the real world, and began scouting out and improving its many applications – first in the resident “Match Day” market for medical school graduates, an approximation physicians had already figured out for themselves. The most lucid short explanation I have seen, by Matthew Yglesias, is here. A longer account, by Leon Neyfakh, of The Boston Globe, is here.  Roth’s important article, “The Economist as Engineer,” is here.  Roth’s chapter, “Deferred Acceptance Algorithms: History, Theory, Practice, in John Siegfried’s Better Living through Economics, is clear, comprehensive and concise. And his personal home page, a model of contagious enthusiasm, is here.

But Shapley’s long career – he began producing profoundly original work in the 1940s and kept it up for thirty years – can’t easily be reduced to a penetrating practical insight. (Here is his citation as a Distinguished Fellow of the American Economic Association.)  Nor can it yet be judged a crowning achievement – more nearly like, perhaps, the keeping of Lindesfarne Abbey than the design of the cathedral at Chartres. The Nobel award assures that Shapley’s story, like that of Nash, eventually will be told – but not for a while with clarity and in detail.

In fact, the youthful Shapley figures prominently, if briefly, in a couple of well-known books:  Sylvia Nasar’s A Beautiful Mind and Robert Leonard’s Von Neumann, Morgenstern, and the Creation of Game Theory.

In Nasar’s book, he appears suddenly as “Lloyd,” a foil to Nash at Princeton when both arrived there, in the autumn of 1950.  “No one could have presented a stronger contrast with the childish, boorish, handsome and uninhibited boy wonder from West Virginia” than Shapley, she writes.  A war hero weatherman (he broke the Japanese code in China), a Harvard man (and son of famous astronomer Harlow Shapley), a brilliant mathematician, the favorite of von Neumann (the inventor of quantum mechanics mathematics and pioneering computer architect who had recently turned his attention to the description of economic behavior): Shapley elicited ferocious envy and adolescent pranks from Nash – and, of course, also provided major motivation. It was presumably the competition with Shapley, and his suite-mate Shubik, which impelled Nash to the burst of creativity that, fifty years later, was the centerpiece of the first official recognition of game theory by the Swedes.

Nash eclipsed, with his own analysis of individual behavior (which he dubbed non-cooperative), the preoccupation with coalitions that was at the heart of von Neumann’s project. He then drifted off into decades of mental illness. (His eventual recovery, thanks to his wife, supplied the essential drama in Nasar’s book.)  Shapley developed some pretty spectacular eccentricities of his own – in particular a sleep cycle based on a 25-hour clock. But he was an active collaborator and kept working into his 60s, contributing several essential ideas to game-theoretic economics .  (He contributed, too, the title of Nasar’s book, at one point speaking to her of Nash’s “keen, beautiful, logical mind.”)

Shapley makes a dramatic entrance in Leonard’s book as well, this time in the summer of 1948. The scene is the Santa Monica, Calif., headquarters of RAND Corp., the top-secret Air Force spin-off charged with developing new doctrines of Cold War offense and defense in the post-Hiroshima nuclear age. The topic is a dogfight between two fighter airplanes.

Von Neumann himself is at the blackboard, expounding, in mathematical terms, the choices facing the pilots:  “Now, if we let F(x) be the density function describing player 1’s mixed strategy, and G(y) be that for player 2, then we can write 1’s expectation as the Stieltjes integral….”  From the back of the room comes a youthful voice:  “No, no! That can be done much more simply.”

Now my heart stood still, [related Hans Speier, the newly appointed head of RAND’s Social Science division], because I wasn’t used to this sort of thing. Johnny von Neumann said, “Come up here, young man.  Show me.” He goes up, takes the piece of chalk, and writes down another derivation, and Johnny von Neumann interrupts, and says, “Not so fast young man. I can’t follow.”

Now, he was right…. The young man was right. Johnny von Neumann, after this meeting, went to [research director] John Williams and said, “Who is this boy?”

He said, “I found him there and there, and I was told he was a very promising young mathematician, so we hired him,”

He said, “How long has he been here?”

“Oh, about six or nine months.”

“And what has he been doing?”

Only John Williams could do this marvelously. He said, “Oh, well, he has written three or four papers, each of which is the equivalent of a doctoral dissertation in mathematics.”

Which was true.  Johnny von Neumann looked at that and gave him – I don’t know – it was something quite fantastic: a special stipend to Princeton of something like that… He was the son of a Harvard professor.

An historian, Leonard was concerned with the wellsprings of game theory, from the first glimmerings of curiosity about the psychology and mathematics of chess in the decades before World War I, to the subtle but dramatic shift in focus that took place in the 1930s and ’40s, at the hands of von Neumann and his collaborator, economist Oscar Morgenstern, in apparent response to the rise of the Nazis and the Soviet Union, the destruction of European Jewry, and the advent of the Cold War. His chronicle took twenty years to write, so extensive was the archival research and interviewing, so punctilious his mastery of the material. It is, as Leonard notes, a detective story of sorts, in which a solitary figure brooding over a chess board gives way to a roomful of strategists arrayed around an enormous board for a war game – monitored by a ring of psychologists manning the rail of a balcony above.

It was in this nexus of military and academic research that the future central figures of game theory made their appearance – John Nash, Lloyd Shapley, Martin Shubik, John Harsanyi, and Robert Aumann – to be succeeded by an exponentially growing progeny inhabiting a new discipline.  The names von Neumann and Morgenstern are known to them all, but few are aware of the complex drama underlying the creation of the theory of games.

Leonard’s was well underway by 1994, but Nasar’s  book was called into being by the Nobel recognition of Nash, Harsanyi and Reinhard Selten.  She was the New York Times reporter assigned to cover a prize to an economist whose name was virtually unknown beyond the narrow boundaries of his field.  This was strategic storytelling at its most exalted, a snowball carefully lobbed by the Swedes on the upper slopes of fame that precipitated a veritable avalanche of public understanding, in the form of her best-selling book four years later, and an Academy Award-winning feature film three years after that.  (Until recently, a photograph of actor Russell Crowe, not Nash himself, decorated the cover of the steady-selling paperback edition.)

What a miracle that book was! It calls into sharp relief what was possible in the last days of the newspaper monopoly when reporters could, within limits, follow their noses as they pleased. But this year’s prize makes clear, it was the first word on the entry of game theory into economics, not the last.  Perhaps Nasar will tackle Shapley’s story, though probably not, for her last book, Grand Pursuit: The Story of Economic Genius, took her in the direction of literary economics. I asked Leonard last week about his current project.  He is working on the life of E.F. Schumacher, a protégé of John Maynard Keynes, the author of Small is Beautiful:  Economics as if People Mattered, and, it turns out, a very interesting man.  The world can hope that Leonard will return to Shapley when his current task is done. The idea of stability in cooperative theory may correspond to the idea of Nash equilibrium in non-cooperative theory, as the Nobel citation puts it – a situation in which matters cannot be improved, unilaterally or otherwise.  But an analytic framework broadly useful in the world itself has so far proved elusive. The story is far from over.

Meanwhile, a steady stream of important books continues to issue from the little band of historians of economic thought whose headquarters is Duke University:   Mary Morgan’s long-awaited book on the inner logic of economic models, The World in the Model: How Economists Work and Think, has finally appeared. In preparation are Roy Weintraub and Till Düppe’s illuminating fable of the parallel careers of Gerard Debreu and Lionel McKenzie, Craufurd Goodwin on Walter Lippmann, Philip Mirowski on alternatives to neoliberalism after the financial crisis

The Nobel prize this year may well provide another textbook illustration of the symbiosis among the Swedish authorities, journalists and historians.  Stockholm loves a good story.  At least not since Aumann and Schelling in 2005, the Talmudic logician and the intuitive strategist, has there been a pairing in economics like this one.

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