Alvin Roth on Matching Markets
https://qz.com/421547/nobel-prize-winner-alvin-roth-explains-the-hidden-economics-behind-tinder-marriage-and-college-admissions/
Alvin Roth, a professor at Stanford University, is a very rare economist; he is an economist who saves lives. In 2012, he was a co-recipient of the economics Nobel prize, for his work in helping fix a long problem with the market for kidney donations. Roth already had previous experience working with matching markets, in which he reshaped the National Resident Matching program, which matched medical school graduates with hospital internships. Based off of this, Roth devised a new algorithm that helped matching kidney donors to compatible recipients. This system became one of the country’s first kidney exchange clearinghouses. Roth believes his work has lead to 4,000 kidney transplants that may not have occurred before.
This type of market for kidneys being donated is an example of a matching market. Matching markets examine scenarios of matching two distinct sets of groups together. Most matching market scenarios can be analyzed by looking at a bipartite graph, which is when there are two groups of nodes and all edges go from nodes in one group to nodes in the other. A bipartite graph is present in this scenario of kidney donations, as one group of nodes would be the donors while the other group of nodes would be the recipients. Edges in the graph would connect the donors to recipients in which they are compatible with. The best scenario to occur when analyzing matching markets is to see a perfect matching scenario, when all nodes are assigned and every node is linked to what it got assigned to. This is a good thing to occur, as everyone one is linked and matched, and no one is left out. This could occur in the kidney donation realm, as a scenario could arise where there are 5 donors and 5 recipients and each donor matches each recipient perfectly. In matching market theory, the matching theorem states that if a bipartite graph does not have perfect matching, then there must be a constricted set. A constricted set occurs when a group of nodes are only willing to take a set of nodes that is smaller than their group. An example of this in the kidney donation market would be if 3 recipients could only match with two donors. This means that one of the recipients is going to be left out, and has no other donors assigned to him.
In this article, Roth was interviewed by Quartz, where they discussed matching markets and what he has learned throughout his years of experience in the field. Roth mentions how matching markets are a type of market where the price is not set so that supply equals demands and that is why they are so interesting to analyze. He then goes on to discuss how some markets clear very early, and how matching markets can help specific markets clear much faster. Roth then goes on to discuss how he doesn’t view Airbnb and Uber as companies but rather as marketplaces. He states how Airbnb is a matching market between travelers and hosts and Uber is a matching market between travelers and drivers. Later in the interview Roth goes on to talk about how recent technological advancements have made these matching markets much more prominent and needed. The amount of access to matching markets grew drastically once the internet and other technologies emerged.