Lloyd S. Shapley, who shared the 2012 Nobel Memorial Prize in Economic Science for work on game theory that has been used to study subjects as diverse as matching couples and allocating costs, died on Saturday in Tucson. He was 92.

He broke a hip several weeks ago, his son Peter said in confirming the death.

Dr. Shapley, a mathematician and emeritus professor at U.C.L.A., was considered one of the fathers of game theory, which tries to explain the choices that competitors make in situations that require strategic thinking. The “Shapley value,” named for him, is a concept through which the benefits of cooperation can be proportionally divided among participants based on their relative contribution.

He was a close friend and mentor to John Forbes Nash Jr., a mathematician and Nobel laureate who had schizophrenia. Sylvia Nasar, a former reporter for The New York Times, devoted a chapter in her 1998 biography of Mr. Nash, “A Beautiful Mind,” to the men’s friendship. (The book was adapted for a 2001 film.)

Ms. Nasar said the book’s title was suggested by a remark by Dr. Shapley. “He was obnoxious,” Ms. Nasar quoted him as saying about Nash. “What redeemed him was a keen, beautiful, logical mind.”