I have a taste for collective biography; I think it’s generally the best way to tell a story, at least once its broad outlines are known. I am currently reading one popular account, The Generals: American Military Command from World War II to Today, by Thomas Ricks, and have two more on my bedside table (The Philosophical Breakfast Club: Four Remarkable Friends Who Transformed Science and Changed the World, by Laura Snyder; and The Clockwork Universe: Isaac Newton, the Royal Society, and the Birth of the Modern World, by Edward Dolnick). Before long I imagine that someone will hazard an essay about lives of the various builders of the digital revolution (as opposed to its architects), chief among them Bill Gates, Steve Jobs and Tim Berners-Lee, all three of them born in 1955. Let’s hope the author first reads Between Human and Machine: Feedback, Control, and Computing Before Cybernetics, by David Mindell.
I know that our deeper understanding depends on scholarship, and that good scholarship requires both the passage of time and the expenditure of great effort. Ricks depends in part on Eisenhower’s Lieutenants: The Campaigns of France and Germany 1944-45, by Russell Weigley, and Dolnick’s account is founded on countless studies of the events of the emergence of modern science, including Dirk Struik’s splendid A Concise History of Mathematics. Ricks and Dolnick are journalists. It’s when a professional historian goes straight to pop, as in The Philosophical Breakfast Club, that context suffers and the narrative trails off. So I don’t expect a really trenchant account of the digital revolution to emerge for many years.
The book I yearn to read some day is a deep examination about the way that psychology and strategic behavior came to economics in the twentieth century, in the guise of game theory. So far its leading characters pop up as individuals, either the subjects of biographies (John von Neumann in books by Steve Heims and Norman Macrae) or recipients of Nobel Prizes – John Nash eighteen years ago (not long thereafter the subject of Sylvia Nasar’s A Beautiful Mind), and now Lloyd Shapley. If you had gotten up early yesterday morning, you could have seen, streaming live from Stockholm, via the Internet, the 89-year-old Shapley, an old man grasping a sheaf of notes, attempting to deliver a stripped-down talk about one aspect of his work, intermittently puzzled and confident, until a wave of applause relieved him of the need to persevere.
Against long odds, Shapley won the game that senior players sometimes call “Beat the Reaper.” Considering that he and Nash met as young men in the extraordinary hothouse that was the Princeton University Department of Mathematics in the days soon after World War II he is fortunate indeed. In a setting dominated by the polymath von Neumann, he and Nash quickly shouldered aside the founding father and divided up among themselves and their friends the competing programs that game theorists have pursued ever since.
You have to admire the alacrity with which the committee of the Royal Swedish Academy of Sciences acted, pairing Shapley, of the University of California at Los Angeles, with the vigorous, young Alvin Roth, who just left Harvard for Stanford University (a stripling at 60.) They did much the same in 1996, with William Vickrey, 82, of Columbia University; and, in 2007, with Leo Hurwicz, 90 of the University of Minnesota, pairing them in each case with much younger men. In Hurwicz’s case they beat the Reaper by less than a year; Vickrey died a few days after learning of his award, his heart burst from the renewed excitement of the chase. On the other hand, Fischer Black and Zvi Griliches expired before they could collect their due.
By citing Roth, the Swedes licensed a forceful spokesman for applied economics: the design of markets in which you must be chosen as well as bid: kidney transplants, admission to sought-after schools, jobs in fancy hospitals. Even houses in desirable neighborhoods sometimes change hand these days on the basis of letters detailing the purchasers’ intentions for them. The prize-awarders achieved their purpose by focusing on a narrow portion of the salient advanced by Shapley, rather than mapping the salient itself and dwelling on features, leaving much of the story yet to be told, but never mind. It’s another combination prize, half of it about tracking the history of thought, the other half resembling a museum show or gallery exhibition of the work of a dominant contemporary artist, an illustration of theory in practice, without overmuch concern for the linkages between the one and the other.
The problem with the prizes is that they obscure the networks that have led to them, with countless others left out. Characteristically, the last slide of Roth’s lecture yesterday contained the photographs of fifteen or twenty collaborators who helped turn market design into one of the most exciting fields in economics: surgeons, medical administrators, educators, junior colleagues. Such a slide, had it been prepared to accompany Shapley’s lecture, would have included a very different dozen or two collaborators, beginning with the mathematician’s famous father, the Harvard astronomer Harlow Shapley, who was a story in his own right, having successfully described in 1918 the size of the Milky Way galaxy and determined our sun’s position in it, only then to fight and lose a lifelong battle with Edwin Hubble about what lay beyond the boundaries of our galactic home (nothing, Shapley said). Three other contemporaries whom the younger Shapley met first atPrinceton, back in the day, would stand out.
There would be David Gale, who died in 2008. at 86, Shapley’s mathematician collaborator on the 1962 paper “College Admissions and the Stability of Marriage,” which was the beginning of the skein of work for which this year’s prize was given. Had he lived a little longer, Gale might well have shared in the award. But there seemed nothing unfulfilled about Gale’s life, which was described in this excellent article by the University of California at Berkeley (where he taught for forty years), as a passionate father, puzzle-monger, avid skier, tennis player, traveler and jazz aficionado. (He kept an office in the Ecole Polytechnique inParis as well.)
Then there is Herbert Scarf, 82, ofYale University, Shapley’s co-author on a key paper in 1974, “On Cores and Indivisibility.” Scarf’s contribution to the study of traditional one-sided markets, which is the way the process of kidney exchange is understood, was discussed at some length in the long citation that accompanied the Nobel award. Unexamined, however, was Scarf’s forty-year quest to achieve a satisfying mathematical description of economies in which increasing returns, meaning falling costs, play a prominent role. Such increasing returns, or economies of scale, exist everywhere in the modern world, at least up to a point. Yet a satisfying framework for examining them so far had eluded mathematical economists, including Scarf. The editor of his collected papers quotes a Chinese poem in this connection: “An old war-horse may be stabled, yet still it longs to gallop a thousand miles; and a noble-hearted man, though advanced in years, never abandons his proud aspirations.”
Finally there is Martin Shubik, 86. Shubik, too, collaborated with Shapley often over the years; their 1971 paper on the “assignment game” was a key step in the clear statement of the line of work for which the prize was given. “He was a superb mathematician, and I had a good economic intuition,” Shubik says of Shapley; “together we made a very good mathematical economist.” But Shubik has work of which he is more proud. His 1959 article, “Edgeworth Market Games,” was the first to relate a truly economic concept (the contract curve) to a game-theoretic concept (the core), according to Eric Gordon, and so formed a bridge which game theorists have been crossing ever since. By the time he and Shapley stated the connection formally ten years later, in “On Strategic Market Games,” Shubik’s future was assured. It was Shubik who apparently campaigned successfully for Shapley for this year’s prize.
If they live long enough, both Scarf and Shubik may stand a chance for prizes of their own – Scarf for the algorithms he devised that permit general equilibrium outcomes to be computed for the purposes of estimating the effects of trade (where the problem of increasing returns has proved especially acute); Shubik for the connection between his market games and the nature of money. But the odds are against them. They’ll need a younger partner whose work is not apparent yet.
Meanwhile, the good news, as noted here before, is the presence on the scene of Robert Leonard, of the Université du Québec à Montréal. Von Neumann, Morgenstern, and the Creation of Game Theory: From Chess to Social Science, 1900-1960, carried the story of game theory to just about exactly the point at which the consortium with economics began in earnest. That book took him fifteen years. Leonard now is occupied with a biography of E.F. Schumacher, the technical economists turned Small-is-Beautiful philosopher – an important story in its own right. When Leonard is finished, there will still be plenty of time to undertake the deep collective biography that the second generation of game theorists and their economist counterparts deserve. They, too, changed the world.