Lloyd S. Shapley, who shared the 2012 Nobel Prize in economic sciences for developing the theoretical underpinnings of methods for matching people with limited resources, including organ donors with patients, students with schools and doctors with hospitals, died March 12 at a nursing home in Tucson. He was 92.

A longtime researcher at the Rand Corp. think tank in Santa Monica, Calif., Dr. Shapley was at his death a professor emeritus of economics and mathematics at the University of California at Los Angeles. His son, Peter Shapley, confirmed the death and said the cause was complications from a broken hip.

Known as a major contributor to theoretical and mathematical economics, Dr. Shapley was regarded as one of the titans of game theory.

That branch of mathematics concerns itself with the conceptual underpinnings of the choices and interactions, conscious and unconscious, large and small, personal and institutional, that people make every day of their lives.

Game theory is an apt title for the field, because it implies the element of competition involved in the choices governing human lives and institutions; most choices involve or imply winning and losing, success and failure, satisfaction and discontent.

“Game theory, I think, was made for me, because I was always messing round with great big game-like models, the sort of thing that now they call ‘Dungeons and Dragons,’ ” Dr. Shapley once said. “I’ve always enjoyed the mathematics of it.”

There is no Nobel in mathematics. In 2012 Dr. Shapley shared the economics Nobel with Alvin E. Roth, then of Harvard University, for contributions that spanned mathematics and economics. Dr. Shapley contributed the mathematics. “I never, never in my life took a course in economics,” he said.

In many situations treated by game theory, such as those involving economic life, money may be used as the measure of wins and losses. Dr. Shapley concerned himself with situations in which financial incentives were often out of the picture. Nor was there unrestricted trading, with its almost infinite possibilities.

Rather it might be a matter of maximizing stability in systems of matching up members of pairs, based on innumerable individual transactions in which all choosers must also be chosen.

One of the criteria for success in such transactions is stability; that is, each side in a transaction must be satisfied and neither is to be left wishing that a different choice had been made.

One of the examples given of the Dr. Shapley’s work in this area has been given the name of the stable marriage theorem. Although perhaps unrealizable in true life situations, it involves creation of a formidably logical mathematical system for matching an unlimited number of prospective husbands and wives in such a way as to leave none with regrets.

It was the mathematics behind all this that fascinated Dr. Shapley. “If there’s simply an interesting application,” he said, “well, maybe someone else can do it. . . . The mathematical discovery is the really exciting part.”

Formally, the Royal Swedish Academy of Sciences awarded the Nobel for what it called “the theory of stable allocations and the practice of market design.”

In that work, Peter Shapley said, his father “came up with the method.” The origins were a paper from the early 1960s that laid out the “Gale-Shapley algorithm,” a collaboration between Dr. Shapley and mathematician David Gale. Roth applied Dr. Shapley’s work to real-life problems.

Lloyd Stowell Shapley was born in Cambridge, Mass., on June 2, 1923. He was one of five children of Martha Betz and noted Harvard astronomer Harlow Shapley.

From boyhood, Dr. Shapley’s mathematical aptitudes showed themselves. Against older siblings, he was said to be unbeatable in mathematical games by age 6 because of his knowledge of logarithms. He was a 1940 graduate of Phillips Exeter Academy, a private school in New Hampshire, and then enrolled at Harvard University.

In 1943, amid World War II, he was drafted into the Army Air Forces in China and helped crack a Soviet meteorological code that was critical in planning bombing raids over Japan as dangerous fronts moved eastward from Siberia.

The Soviet Union was allied with the United States against Germany but was officially neutral for much of the war against Japan.

Dr. Shapley, who received the Bronze Star for his military work, completed his Harvard degree in 1948 and received a doctorate in mathematics from Princeton University in 1953.

At Princeton, he befriended mathematician and game theorist John F. Nash Jr., another future Nobel laureate in economic sciences. Dr. Shapley’s description of Nash as possessing “a keen, beautiful, logical mind” provided the title for Sylvia Nasar’s biography of Nash — “A Beautiful Mind” -- and the subsequent film version. Nash, who struggled with mental illness, died last year in a car accident, along with his wife.

Dr. Shapley worked at Rand Corp. from 1954 to 1981 and thereafter at UCLA.

His wife, the former Marian Ludolph, who spent many years as a computer programmer at Rand, died in 1997 after 42 years of marriage. In addition to his son Peter, of Tucson, Dr. Shapley is survived by another son, Christopher Shapley of San Jose del Cabo, Mexico, and two grandchildren.

In their paper, “College Admissions and the Stability of Marriage,” a fundamental part of the Nobel-winning work, Gale and Dr. Shapley concluded by asking just what mathematics is.

In the paper, published in the American Mathematical Monthly, which is pitched at a wide range of readers, the two said math does not require a “head for figures.” Instead, they argued, it demanded the ability to fashion a sufficiently precise argument and to follow “a moderately involved sequence of inferences.”