The Royal Swedish Academy of Sciences cited the two economists for "the theory of stable allocations and the practice of market design".
Roth, 60, is a professor at Harvard University in Boston. Shapley, 89, is a professor emeritus at University of California Los Angeles.
"This year's prize concerns a central economic problem: how to match different agents as well as possible," the academy said.
Shapley made early theoretical contributions to the field of study, and Roth took it further by applying it to the market for US doctors.
The economics prize was created by the Swedish central bank in Nobel's memory in 1968, and has been handed out with the other prizes ever since. Each award is worth 8 million Swedish kronor, or about $1.2 million.
Recent winners of the Nobel Memorial Prize in Economic Sciences, and their research:
2012- Americans Alvin Roth and Lloyd Shapley for the theory of stable allocations and the practice of market design.
2011- Americans Thomas Sargent and Christopher Sims for their research on cause and effect in the macro economy.
2010- Americans Peter Diamond and Dale Mortensen and Christopher Pissarides, of Britain and Cyprus, for their analysis of markets with search frictions.
2009- Americans Elinor Ostrom and Oliver Williamson for their analysis of economic governance.
2008- American Paul Krugman for his analysis of trade patterns and location of economic activity.
2007- Americans Leonid Hurwicz, Eric S. Maskin and Roger B. Myerson for laying the foundations of mechanism design theory.
2006- American Edmund S. Phelps for furthering the understanding of the trade-offs between inflation and its effects on unemployment.
2005- Robert J. Aumann, of Israel and the United States, and American Thomas C. Schelling, for their work in game-theory analysis.
2004- Finn E. Kydland, Norway, and Edward C. Prescott, United States, for their contribution to dynamic macroeconomics.
2003- Robert F. Engle, United States, and Clive W.J. Granger, Britain, for their use of statistical methods for economic time series.
2002- Daniel Kahneman, United States and Israel, and Vernon L. Smith, United States, for pioneering the use of psychological and experimental economics in decision—making.
2001- George A. Akerlof, A. Michael Spence and Joseph E. Stiglitz, United States, for research into how the control of information affects markets.
2000- James J. Heckman and Daniel L. McFadden, United States, for their work in developing theories to help analyze labor data and how people make work and travel decisions.
1999- Robert A. Mundell, Canada, for innovative analysis of exchange rates that helped lay the intellectual groundwork for Europe’s common currency.
1998- Amartya Sen, India, for contributions to welfare economics, which help explain the economic mechanisms underlying famines and poverty.
1997- Robert C. Merton and Myron S. Scholes, United States, for developing a formula for the valuation of stock options.
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