Selling your kidney to someone in need is illegal in the United States. Apparently, giving up an organ at a market price is deemed unethical, or “repugnant.” As a result, the market doesn’t work because the price is too low. Well, it’s effectively zero.

To overcome this “market failure”, economists have attempted to engineer a “market” without prices that efficiently matches up kidney donors with recipients. Alvin Roth, along with Lloyd Shapley, won the Nobel Prize in 2012 for this endeavor.

The Buildup

Before humans used prices and currency to trade goods and services, they would use a bartering system. For example, if I had a bunch of berries, but I also wanted some corn, I would need to match with someone who wanted some berries and had a bunch of corn to give up. However, the problem is that I would need to find someone who wanted berries and had corn to spare. This can be rather inconvenient to satisfy your wants and needs! The pricing mechanism in a market helps overcome this annoyance. With prices, you can just choose what you want, throw some money at it and it’s yours. (It’s crazy how we take this for granted sometimes.)

However, prices might not work as cleanly in some markets. In the job market, it’s not like you can just show up at Amazon, tell the manager how much your labor is worth, and start working. You have to apply, interview, pray, and after all that, you still may not get the job. The same messiness applies to universities. Roth uses the example, “Harvard and Stanford don’t raise tuition until just enough applicants remain to fill the freshman class.” They keep the prices low so that a bunch of students apply allowing them to be selective with who they admit.

Roth calls these “two-sided matching markets” which are more like romantic courtships, with a lot of wooing involved.

“You’re my number 1.” “You’re my maybe.” <3

Deferred Acceptance, aka “maybe”

This idea comes from Shapley and his colleague David Gale, when they proved in 1962 that for any equal number of men and women, you are able to solve the “stable marriage/matching problem”. It is stable because at the end of the process, neither hubby nor wifey want to leave their marriage for someone else.

In the first round, each unengaged man asks his number one pick if she’ll marry him. If the man happens to be the woman’s number one pick, she responds with a maybe. All the other dudes get denied. The next round, the unengaged men propose to their number one picks (even if the women are engaged already). If the woman prefers this new guy, she again, responds with a maybe. This process is iterated several times until everyone is hitched.

The maybe in this process is what allows for stable matches to occur in two-sided markets. It defers confirming a match until we are sure that everyone is with their best pick given what’s left. Then everyone gets married at the same time. Nothing more romantic than a group wedding!

Kidney transplants and group marriages

This type of mechanism can work for kidneys too. They have to make the match and do the surgeries at the same time. Thanks to Roth (in the yellow smock) and fellow economists, computer algorithms can handle not only matching kidney donors and recipients, but also hospitals and surgeons to perform the surgery. (Side note: this type of market design also matched the young surgeons, fresh out of school, with the hospitals they work at.

Roth watching a kidney transplant in action

Roth’s work helps markets that are near and dear to us that are plagued with some kind of roadblock to run a bit smoother. He’s applied his design to dating, public schools, healthcare, and labor markets.

Though we should probably warm up to the idea that selling our organs can help save numerous lives, the two-sided matching market-engineering may be our most preferred pick.

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