Since we have talked about stable matching in class, I thought it would be essential to take a look at the theory of the Nobel prize winners from 2012, Lloyd Shapley and Alvin Roth, who won the prize in economics talking about the stable matching. They approached their studies based on the abstract theory from 1960s and empirical work 1980s in order to focus on the application of the theory on our real world today.
Talking about the prices and the market-clearing property in class, there is a market clearing if prices adjust until supply equals demand and a perfect matching of buyers and sellers is approached. Even though this works out in many cases, there exist situations where the standard market mechanisms encounter problems and resources cannot be allocated most efficient. That is why the economists invented the “Gale-Shapley algorithm” which is based on an abstract idea. In general, Lloyd Shapley investigated the concepts of the game theory in the 1950s and 1960s, based on the concept of stability. David Gale specialized on the matching theory. The biggest challenge in creating real-world models is the creation of stable matching’s where individuals do not gain from further trade.
As an example, they examined the matching of partners where men propose to women and the other way round. They investigated that it makes a big difference if women or men have the right to propose.”If the women propose, the outcome is better for them than if the men propose, because some women wind up with men they like better, and no woman is worse off than if the men had been given the right to propose.” ( Stable matching: Theory, evidence, and practical design). In reverse if man propose, women have a worse outcome from their perspective.
Moreover, they analyzed the market of doctors and how a stable matching between doctors and hospitals can be approached. Evidence for the unstable allocation in the past can be seen in the National Resident Matching Program (NRMP) found in 1950s, which was introduced to create stable matches between doctors and hospitals based on the Gale-Shapely algorithm.
Overall, we can see the significance of the Gale-Shapely algorithm, finding solutions to achieve stable matches. There exist many fields where this theory finds its application. Stable matches are the goal and can be reached in many ways through a price adjustment, but there also exist other fields where the price mechanism does not apply or is inefficient. Furthermore, we can see that in some fields it is necessary to introduce institutions like the NRMP to find best matching solutions.
Please feel free to click on the link to read more about further examples that were investigated or to take a closer look at the matching of males and females.