This is a share of a great post from Presh at Mind Your Decisions on matching markets. Unlike the market for slices of pizzas, matching markets are characterized by two groups of agents (buyers and sellers, of sorts) who need to be properly matched up to engage in a transaction. Think of individuals in need of kidney transplants and kidney donors as participating in a matching market. Same with applying to med school or finding a mate (try participating in that market if you don’t have a “match” on the other side!)
Perhaps surprisingly, matching markets often function in unique and counterintuitive ways. Presh brings together two of these results in one post: 1) Why is it tough for PhD scientists to find jobs? 2) In China, why do women (particularly educated women) have a tougher time finding a mate? In both matching markets, conditions seem to favor each of these groups, making it easier to find a “match”, whether that match is the right employer or a husband. So, why the problem?
Matching down. In the Chinese marriage market, for example, men tend to “marry down,” marrying a woman one “ranking” below himself. Here’s Presh:
Suppose the women still want to have the highest ranked mate. But let’s change the rule for slightly. Imagine that the men want the highest matethat is ranked lower than they are. In other words, they are “matching down.”
What will happen in this game?
(Let’s label the rankings with a gender, so men are 1m, 2m, 3m, 4m, and women are 1w, 2w, 3w, 4w).
We now think about the game from the male perspective. The male ranked 1m will only be interested in matching with the women ranked 2w, 3w, or 4w. The man will pick the woman ranked 2w, and she is fine matching with the highest ranked man. So the two match, and we have 1m matched with 2w. Similarly, there will be a match between 2m and 3w and another match between 3m and 4w.
Who’s left out? The unpaired people are the lowest ranked man, 4m, and the highest ranked woman, 1w. If the highest ranked woman does not find the match suitable, she may stay unmatched.
Matching models can function in many different ways, based on what drives the matching market. In this case, it may be cultural norms about marriage which drive men to “marry down” and result in the “leftover women” phenomenon.
[Follow up: Here’s an article on Economix relaying some recent research revealing that couples in the U.S. are more inclined in recent years to marry someone with the same level of educational attainment as them. They discuss implications related to income inequality therein.