The short answer is that’s it’s not necessarily a good market for either one. And this is quite a puzzle because both are in short supply and should be highly desired.

Let’s start with America. The media and politicians often talk about a shortage of American scientists and engineers. If that were the case, then that would mean PhD scientists should easily be able to get highly-paid jobs after graduation. But the truth is most are having trouble finding employment. Half of PhDs don’t have employment by graduation, and though almost all do eventually get jobs, they often are competing for lowly paid postdoc work. Why is the market for young scientists so awful?

Now let’s switch gears to China. The one-child policy and desire for male children has led to a skewed sex ratio, resulting in a country with 34 million more men than women. In other words, there is an excess number of men competing for a limited number of brides. Women, and educated women, would presumably have bargaining power in the “market for marriage.” And yet, the statistical trend for some women is precisely the opposite. As one paper points out: “In the past few decades, there has been a rise in the number of single, unmarried Chinese professional women, which is known as the sheng nu, or ‘leftover women’ phenomenon.” How is it possible there are “leftover women” in a country with millions of more men?

In both cases, it appears there is a bit of game theory that could explain why the highly educated are getting left out.

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"All will be well if you use your mind for your decisions, and mind only your decisions." Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon. .

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The game of matching

Imagine a matching game that involves four men and four women. Suppose the four men are ranked in order of desirability as 1, 2, 3, and 4. And do the same thing for the women. Imagine everyone can understand the ranking, and that both men and women wish to match with the highest ranked mate as possible. How will this game play out?

The answer is simple, and it’s an example of positive assortative mating. The woman who is ranked 1 has a lot of power in this game. This person can choose to be with any of the four men–as they are all trying to match with the highest woman. But since the woman wishes to match with the highest ranked man as well, she will pick the man who is ranked 1. So the man and women ranked 1 will match and be out of the market.

What happens next? Well now the woman originally ranked 2 is the highest ranked remaining woman. She can be with any remaining man, and so she will choose to be with the highest rank man, ranked 2. Thus the 2’s match up, and similarly the 3’s and the 4’s will match up as well. Nothing that exciting in the model.

But what will happen if the game is slightly changed?

The game of “matching down”

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 mate that 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.

The connection with PhDs

In a blog post for The Chronicle of Higher Education, Chand John writes about the difficulty of trying to get a job in industry after getting a PhD.

I faced it myself after getting my master’s and doctorate in computer science from Stanford University, where I built software that revolutionized the study of human movement, became an early expert and core developer of software featured in Scientific American, and was one of four Ph.D.’s chosen from Stanford’s engineering school for a research award. …

[After preparing properly for jobs, a hard truth came down] Despite having programmed computers since age 8, I was rejected from about 20 programming jobs.

Now there could be many reasons that he couldn’t find a job. But might the idea of “matching down” play a role?

I tried to find articles on this topic and just couldn’t. So perhaps my intuition about this is really wrong. But I base this on my own personal experience of working in consulting, considering getting a PhD, and having friends who have gotten PhDs.

I imagine the job market is something like a matching game. Companies are ranked in terms of desirability, and job applicants can be ranked in terms of education degrees. If companies hired the most educated, the job market would favor the highest educated.

But what seems to happen is a type of “matching down.” The best consulting companies hire people with MBAs from the best schools, the next best hire MBAs from the next tier, and the remaining companies hire a mixture of MBAs and college graduates.

Who gets left out? That would be the highest educated PhDs, who have trouble competing for a limited number of academic positions and find it hard to work in industry.

Leftover women in China

How does the matching game relate to educated women in China? The answer has to do with a common custom in China of “marrying down,” in which a man tends to marry a woman of equal or lesser status (or in other words, the women tend to “marry up”).

In an interview with Public Radio International, one educated woman, Huang Yuanyuan, offered up her theory on the phenomenon of leftover women, which is precisely the equilibrium of the matching game above.

There is an opinion that A quality guys will find B quality women, B quality guys will find C quality women, and C quality men will find D quality women…The people left are A quality women and D quality men. So if you are a leftover woman, you are A quality. H/T: The Economist

The surprising result is that A quality women tend not to get married in a country where there are more men than women.

The matching game illustrates an important lesson about skills. One would think it’s always good to be ranked higher in matching games. But the A quality women in China and many PhDs in America end up being “leftover”, not in spite of their high quality, but precisely because of their high quality. Apparently sometimes it is better to be second best.