15 October 2012
Last updated at 12:03 GMT
The Royal Swedish Academy of Sciences cited the US academics for their work on the "theory of stable allocations and practice of market design".
The work is concerned with the best possible way to allocate resources, such as in school admissions or organs to patients who need transplants.
Mr Roth is a professor at Harvard and Mr Shapley teaches at the University of California in Los Angeles.
"Even though these two researchers worked independently of one another, the combination of Shapley's basic theory and Roth's empirical investigations, experiments and practical design has generated a flourishing field of research and improved the performance of many markets," the Academy said.
Stable matching Mr Shapley and his colleague David Gale in 1962 laid down a theory for how best to match demand and supply in markets with ethical and legal complications, such as admitting students to public schools in the US.
If these particular markets were just left according to price, then you would get what economists refer to as market failure.
This original work developed into the Gale-Shapley algorithm, which aims to ensure "stable matching" or the best possible outcome for both sides. "An allocation where no individuals perceive any gains from further trade is called stable," the Academy explained.
The two economists worked independently on the same work
This is a key pillar in co-operative game theory, an area of
mathematical economics that seeks to determine how rational individuals
choose to co-operate.
In the early 1980s, Alvin Roth set out to study the market for newly-qualified doctors and study stable matching in the real world.
This was a problem as a scarcity of medical students - such as that which existed in the US in the 1940s - forced hospitals to offer internships earlier and earlier, sometimes several years before graduation, meaning that a match was made before they could produce evidence of their skills and qualifications.
A clearing system was set up to try to better match medical students and hospitals. In a paper from 1984, Mr Roth studied the algorithm used by this clearing house and discovered that it was very close to the Gale-Shapley algorithm, showing that it applied in real-life situations.
The awards continue a strong US run of victories in the category of economic sciences.
Forty-three prizes in economics have been awarded every year since 1969.
The prize was not part of the prizes set out in Alfred Nobel's will and was set up in 1968 by Sweden's central bank.
The work is concerned with the best possible way to allocate resources, such as in school admissions or organs to patients who need transplants.
Mr Roth is a professor at Harvard and Mr Shapley teaches at the University of California in Los Angeles.
"Even though these two researchers worked independently of one another, the combination of Shapley's basic theory and Roth's empirical investigations, experiments and practical design has generated a flourishing field of research and improved the performance of many markets," the Academy said.
Stable matching Mr Shapley and his colleague David Gale in 1962 laid down a theory for how best to match demand and supply in markets with ethical and legal complications, such as admitting students to public schools in the US.
If these particular markets were just left according to price, then you would get what economists refer to as market failure.
This original work developed into the Gale-Shapley algorithm, which aims to ensure "stable matching" or the best possible outcome for both sides. "An allocation where no individuals perceive any gains from further trade is called stable," the Academy explained.
The two economists worked independently on the same work
In the early 1980s, Alvin Roth set out to study the market for newly-qualified doctors and study stable matching in the real world.
This was a problem as a scarcity of medical students - such as that which existed in the US in the 1940s - forced hospitals to offer internships earlier and earlier, sometimes several years before graduation, meaning that a match was made before they could produce evidence of their skills and qualifications.
A clearing system was set up to try to better match medical students and hospitals. In a paper from 1984, Mr Roth studied the algorithm used by this clearing house and discovered that it was very close to the Gale-Shapley algorithm, showing that it applied in real-life situations.
The awards continue a strong US run of victories in the category of economic sciences.
Forty-three prizes in economics have been awarded every year since 1969.
The prize was not part of the prizes set out in Alfred Nobel's will and was set up in 1968 by Sweden's central bank.
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