Tuesday, December 18, 2012

David Warsh on Lloyd Shapley and his colleagues

After a head feint towards another topic, David Warsh writes about Lloyd Shapley and his colleagues David Gale, Herb Scarf, and Martin Shubik.

"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. "
"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 inthis 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."

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