In 2012, Lloyd Shapley and Alvin Roth received a Nobel Prize for their work in market design- in particular, work with matching situations- think organ donors and recipients. This article references the Gale-Shapley algorithm. This algorithm was created in order to find the best stable match possible in a scenario where members of one group must be matched with members of another group. The Gale-Shapley algorithm looks at the preferences of each member in both groups (for example, a group of hospitals and a group of residents which they must be matched to) and generates a list of pairings which constitute a stable matching- that is, there is no pairing such that both members of the groups can be placed in a better match based on the other pairings.
This correlates to our studies of matching markets, where we must work to generate matchings that correlate with market preferences- that is, we must work to create a matching where most of the members are satisfied with their situation. A bipartite graph is a good representation for the scenario occurring in the Gale-Shapley algorithm, since both groups can be recreated as a bipartite graph. In particular, the Gale-Shapley algorithm can be used to create matching within preferred seller graphs, which states specific ordered preferences for each node.
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Trading kidneys, repugnant markets and stable marriages win the Nobel Prize in Economics