Playing with Matches
The Economics of Matchmaking Part II: Matching Functions
This is part 2 of a series on the economics of matchmaking. Before you read this, get up to speed with part 1.
1. It Takes Two
Our lives are built on a series of searches. We gather information, and set our standards. We hunt for jobs, apartments, and partners. We weigh our options. Finally, we make our choice and hope for the best.
That’s only half the story.
You get to choose. But they have to choose you too.
You can polish that resume until it gleams. Nail every interview question. A week later they’ll say: "We've decided to move forward with another candidate.”
You like them, but they like someone else. Tough.
In the economy of relationships—be it professional or romantic—both sides have to choose each other.
This two-sided nature of matching is what makes human connections so complicated. Unlike buying a cup of coffee, forming relationships requires mutual selection. Both sides must say yes.
This is where matching functions come in.
2. Matching Function: A Black Box of Chocolates
Think of a matching function as an invisible machine. Just like how a production function in economics combines labor and capital to create goods. A matching function describes how meetings between people create relationships.
Feed it prospective employees and would-be employers, you get jobs. For single men and single women, the matching function pairs them and makes new couples.
Economists study matching functions because they help explain big patterns in society: unemployment rates, marriage trends, business formation, even friendships.
The function explains this match-making process with a simple mathematical relationship. But the conversion rate isn't 100%. Most job interviews don't lead to offers. Most first dates don't become marriages. Most networking events don't yield business partnerships. You can’t quite know what you’re going to get.
The function itself is like a black box—to say that matching works in mysterious ways. We don’t see the complex human drama inside—but we can observe its inputs (meetings) and outputs (relationships) and figure out how it works.
3. Joint Ventures: A Theory of Marriage and Economic Behaviour
To understand what makes matches, economists look at why people choose each other.
Gary Becker, a Nobel laureate, viewed marriages as two-person startups. where households function like small factories. Partners pool their inputs—time, money, skills, and effort—to produce valuable outputs that enhance their lives.
The inputs flowing into this household factory include: their skills, their labor time, and economic resources.
The outputs this household factory produces include: home-cooked meals, social status, wealth accumulation, children and child-rearing.
In Becker’s model, a couple will only form if their joint output exceeds what they could produce separately, plus all the other opportunities they're giving up. Think of it as relationship ROI: if the partnership doesn't create value, why commit?
These "gains from marriage" (economists' romantic term) come from familiar business synergies:
Division of labor: One does the taxes, the other sends the kids to piano.
Risk sharing: If one person loses their job, the household doesn't collapse.
Cost Efficiencies: Buying in bulk, splitting rent, sharing Netflix password. Costs get distributed across two people.
Romance can be irrational, but commitment is serious business.
This framework applies outside marriages too.
Business partnerships form when each party brings added value to the table. Job matches happen when a worker's skills complement a company's needs. Even friendships often involve some exchange of value.
4. A Sort of Selection
The matching function doesn’t just randomly pair people up. It's sorting them based on certain traits.
Look at the couples you know. Lawyers court lawyers. Doctors, generally speaking, don’t end up with circus performers. PhD students often date other PhD students. This isn't coincidence—it's positive assortative matching (PAM). Birds of a feather flock together. Like attracts like.
In biology, many species mate assortatively by size, color, or genetic markers. Humans do the same, but with social and economic traits. We see strong PAM across multiple dimensions: ethnicity, religion, education, geography (or physical proximity), tax brackets and age.
This sorting happens because similar traits often amplify each other's value. For example, two high earners can afford a greater standard of living than just a single-income household. The couple can compound their advantages: they can afford to live in a better neighborhood. They have expanded professional networks. They make informed career decisions together. They can invest more for their children, if they have any.
But similarity isn't just about maximizing output—it's opportunity. How else do people meet potential partners? If not through work, school, and social circles.
These environments naturally cluster people with similar backgrounds, education levels, and interests. They are like proxies for proximity. The matching function reflects not just preferences, but the structure of social interaction itself.
Sometimes, opposites attract. This is known as negative assortative matching (NAM).
In biology, an example of NAM would be genetic diversity, as it produces healthier offsprings. In economics, differences create value through specialization rather than amplification. The classic breadwinner-homemaker pairing is one example, where one person specializes in market work while the other handles domestic production. In business partnerships, you might see a visionary paired with an operations expert, or a risk-taker with a risk-manager.
Real matching shows both patterns simultaneously. Partners might match positively on education and race (similar social backgrounds) while matching negatively on personality traits (complementary skills). The matching function efficiently sorts people along multiple dimensions, to form partnerships that maximize value.
5. The Invisible Hand
When economists study matching functions across entire markets—all the marriages in a city, all the job placements in an industry—they find surprisingly consistent relationships. Double the number of single people and job seekers in a market, and you get roughly double the number of matches, adjusted for efficiency.
Of course, the process isn't perfect. Some people remain single after countless dates. Many people cannot find a job when times are bad or good. Market frictions—imperfect information, search costs, timing issues—mean the matching function doesn't work smoothly.
Here’s the thing: nobody is orchestrating these matches. There’s no central planner arranging marriages. There's no algorithm optimizing for all allocations (despite what apps might claim). But the system works.
The system is built on billions of individual choices aggregating into social patterns. An emergent order from this beautiful chaos. Every successful match proves that two people found something in each other is worth more than what they had alone. Every relationship formed adds value somewhere in the system. The matching function is the infrastructure of modern society.
Understanding matching functions doesn't reduce human connection to cold calculation.
The math can track the patterns. But what lights a spark between two hearts remains a mystery.
Refs, Recs & Inspos
Freakonomics
St Louis Federal Reserve: An Economist’s Perspective on the Marriage Market
A Theory of Marriage (Gary S. Becker)