Lloyd Stowell Shapley: In Memoriam
An era is ending and almost all of us who were there at the start of the growth of the theory ofgames have died. Lloyd’s mind, unfortunately left us several years ago when he was felled withdementia. Being the analyst that he was he said to me a year or so before he accepted (with muchmisgiving) the Bank of Sweden’s prize in honor of Alfred Nobel that he was worried that there
were signs that he might be following his father Harlow Shapley, a famous astronomer, who wasfelled by dementia in his 80’s. Lloyd said that his doctor had commented to him that he was too
old to contract Alzheimer’s disease but that he had premonitions about dementia.
Lloyd was born on June 2, 1923 in Cambridge Massachusetts, the fourth child and third son ofHarlow and Martha Betz Shapley who gave up the potential of an independent career to help her
husband at the observatory and to bring up five children. Prior to World War II Lloyd was anundergraduate at Harvard, where according to him he was somewhat bored with academe andmade a bet that if one could be good enough at judging the professor and the subject that youcould get the grade you felt like getting. Thus in order to obtain a D in an exam one might haveto sleep through much of it. He noted that the Harvard examiners were not amused.
World War II had Lloyd swept in as an enlisted man sent to Western China where his task was todecipher Russian codes. He succeeded in breaking them. It is comforting to know that on
occasion a bureaucracy manages to fit a square peg into a square hole.
After the war Lloyd finished his Harvard A.B. and in 1948 joined the newly formed Rand
Corporation. While attending a von Neumann lecture he suggested modifications to the analysis
presented. Von Neumann was sufficiently impressed that he recommended that Lloyd be given aleave from Rand and support to go to The Mathematics Department at Princeton to get his PhD.
He went to Princeton in 1949 and in 1953 obtained his PhD writing on Additive and Nonadditive
Set Functions with his thesis advisor being Albert W. Tucker.
At Princeton he was a Fine Instructor from 1952-54. He was suggested as a potential assistant toAlbert Einstein, but he commented that he saw no point in working for an old physicist who had
made no basic contributions for many years when he was in a period of high productivity
himself. He felt that that type of position would be better occupied by a reflected fame seeker.
Another person took the job.
My first introduction to Lloyd was after the lottery that at that time involved suite and room
selection at the Graduate College at Princeton in September 1949. The random selection had asuite assigned to Shapley, Nash and myself. There were only two bed rooms. Lloyd and I shared
one and Nash had the other. It took us very little time to comprehend that John who was bothyounger and immature gave every indication of being brilliant and being extremely disturbed.
Lloyd regarded himself as essentially a mathematician and his love was pure mathematics, yet inspite of himself he became hooked into game theory and made original and profoundcontributions to every aspect of it. He emerged as possibly the most profound game theorist,beyond von Neumann until now.

Shapley did not generate models in political economy per se, but once he was presented witheven a half-baked model he quickly showed a deep understanding of the problem at hand andtightened both the mathematics of the problem representation and its relevance in application. No
other mathematician working in game theory, to my mind has shown anywhere near his practicalinsights and practical feeling for models in political economy and the social sciences in general
as is evinced in his joint construction of a parlor game called So Long Sucker and a popularboard game called Diplomacy.
In particular I remember the genesis of both the value and core solutions that are both landmarksin the study of games in coalitional form and in application. In formulating the Shapley value
Lloyd wrote the axioms in part at Princeton and in part at his family’s summer home in Sharon
New Hampshire. He had invited me to join them for Thanksgiving. This involved an evening
drive from Princeton and a 2 a.m. arrival at the observatory house at 60 Garden Street inCambridge where chocolate chip cookies and instructions had been left for us on the stairs. We
then proceeded the next day to Sharon. The time there was spent in individual work by all, withLloyd concentrating on his value axioms. There was however a lengthy session on the porchoverlooking the forest in New Hampshire with Harlow Shapley posing a simple problem to us.
He observed that the trees were rocking to and fro violently and he conjectured that this motion
was the cause of the heavy winds we were experiencing. Could we provide him with anexperimental design to be able to prove or disprove this hypothesis?
It appeared to me that the Shapley value had an immediate application to voting in committee
meetings and that it could be of special value in situations where different individuals had adifferent number of votes. We wrote a small paper applying the Value to committee votes andmuch to our surprise the American Political Science Review accepted this paper from two
unknown graduate students in a very few weeks. The value has gone on to be a seminal tool inmany other uses. The development and first applications of the core involved not only commentson the von Neumann Morgenstern stable set solutions and the mathematical work of Don Gillies
but also an understanding of the connections to the work of Edgeworth and to the horse-market
example of Boehm-Bawerk.
Sometime after the publication of the Value solution and after Nash’s publication of his thesis
results on the existence of noncooperative equilibrium points I had the opportunity to talk withProfessor von Neumann. I evinced my enthusiasm for the use of the Shapley Value as a solution
concept to apply to games in coalitional form. He argued strongly against both the value and thenoncooperative equilibrium. Von Neumann felt that the formal mathematical representations
used in the strategic and coalitional forms abstracted so much from the societies they were meant
to represent that it was unreasonable to look for a solution that was a single point. Too muchcontext has been left out to merit narrowing the solution to more than a subset of the outcomes. I
argued that the Shapley value could be looked at as a natural benchmark. His decision to returnto Rand in 1954 was based on considerations that he did not much like teaching but loved
research. The Rand that he worked at in the 1950s and 60s was a very different institution fromRand in the 1980s and Lloyd left to join the mathematics department at UCLA.
In spite of not being directly at a university at the time his first de facto PhD student was Pradeep
Dubey with whom he wrote many joint papers. His only joint book Values of Non-atomic Gamesoriginally published in 1974 was with his colleague, and friend Robert Aumann, although I
regard the book Game Theory in the Social Sciences, I published alone in 1984 as being based
completely on joint work with Lloyd.
Although he was a member of the American Academy and the National Academy and held anhonorary degree from the Hebrew University Lloyd was not a seeker after prizes or celebrations.
At a meeting at Stonybrook held in his honor when asked to speak he commented that he felt thiswas like an end-of-summer, summer camp celebration where there was a prize for everyone, aprize for the slowest runner, a prize for making one’s bed, and so on.
Turning to non-scholarly aspects of Lloyd’s life, he was a highly competent pianist and an avid
folk dancer both at Princeton and Rand. He was also a dedicated Kriegspiel, Chess and Goplayer. It is of note that while he was a good Chess and Go player he was superb and virtually
unbeatable at Kriegspiel. He and his wife Marian were dedicated puzzle solvers. His family life
was close. He and Marian had two Sons, Peter and Christopher and the family lived in comfort in
the Pacific Palisades, complete with swimming pool and a guestroom heavily occupied byvisiting scholars coming to work with Lloyd or by members of a large Shapley clan of relatives.
The loss of Marian to bone cancer was a great blow to him, but he continued to live in the housethey had bought in the 1960s until he succumbed to dementia.
This is possibly not a conventional Memoriam, but it is aimed at being a portrait of some aspectsof a life of a great scholar and a personal friend.
Martin Shubik March 16, 2016