Thursday, May 2, 2013

American Math Monthly reprints Gale and Shapley 1962

The journal is available on jstor and to members, but here is some of the front material. The paper itself is well worth reading, and I've posted a link to an un-gated version below.

A Letter from the Editor 383
Scott Chapman

"...This month, we honor the Nobel Prize-winning accomplishments of Lloyd Shapley. Shapley’s 1962 MONTHLY paper “College Admissions and the Stability of Marriage,” co-authored with David Gale, is well-known to long-time MONTHLY readers. According to Google Scholar, the Gale/Shapley paper has been referenced over 2500 times (among MONTHLY articles, only Li and Yorke’s 1975 paper “Period three implies chaos” has been referenced more). Hence, when the announcement was made late last year that Shapley and Alvin E. Roth had been awarded the Nobel Prize in Economics “for the theory of stable allocations and the practice of market design,” it
was not a surprise that the 1962 MONTHLY paper was cited by The Royal Swedish Academy of Sciences. I did find it surprising that many of the younger members of the MONTHLY Editorial Board were completely unaware of this paper. Vadim Ponomarenko wrote me the following: “The article is not only short and ground breaking, but really well-written and interesting. I think the MONTHLY should republish this article in its entirety.” Thus was born the idea to honor Shapley by reprinting his article.
I thank Ehud Kalai, a long-time colleague of Shapley’s and the James J. O’Connor Professor of Decision and Game Sciences at the Kellogg School of Management at Northwestern University, for offering to write a Foreword to Gale and Shapley’s work.
I believe that his Foreword speaks for itself, but add that the MONTHLY Editorial Board sees the reprinting of Gale and Shapley’s paper as a special opportunity to open this classic piece to a new generation of mathematicians."

Foreword: The High Priest of Game Theory 384
Ehud Kalai

"In “Von Neumann, Morgenstern, and the Creation of Game Theory” [1] Robert Leonard describes a 1948 public lecture presented by John von Neumann at the RAND Corporation in Santa Monica. The lecture was interrupted by a young voice from the back protesting “No! No!, that can be done much more simply!” According to Hans Speier, a director at RAND, you could have heard a pin drop as von Neumann said “come up here, young man. Show me.” The young man goes up, takes the piece of chalk, and writes down another derivation as von Neumann interrupts and says
“not so fast, young man. I can’t follow.” The young protestor was Lloyd Shapley, and following this incident he was awarded a stipend to study game theory at Princeton, a fortunate occurrence for the future of game theory.
More than a half a century later, the 2012 Nobel Prize in economics was awarded to Lloyd Shapley and Alvin Roth. Roth opened his Nobel Prize lecture with the following sentence: “Lloyd, when I began studying game theory your work touched every part of it and shaped it, and you were an inspiration not just for me but for the whole generation of game theorists that followed you. . . .” Robert Aumann, the 2005 Nobel Laureate game theorist who often introduced Shapley as the “High Priest of Game Theory,” stated in his Nobel Prize Lecture that Lloyd Shapley is the “greatest game theorist of all times.”...

College Admissions and the Stability of Marriage 386
D. Gale and L. S. Shapley

Read it or re-read's a great paper. Here's an ungated version.

1 comment:

PLW said...

Thanks for this. I'd always heard these results but never actually read the paper. I especially liked the comment at the end on how to use the marriage market to illustrate to laymen what mathematicians do.