peteg's blog - noise - books - 2015 10 28 Roth WhoGetsWhatAndWhy

Alvin Roth: Who Gets What — and Why: The New Economics of Matchmaking and Market Design. (2015)

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Kindle. This is Alvin Roth on his life's work, viz matching markets. He begins by carefully distinguishing these from commodity markets, which are constructed by lumping products that are sufficiently similar into buckets that are traded identically. (Apparently this was the central innovation of the Chicago Board of Trade a long time ago.) Specifically these tend to ignore the identities of the producers and consumers, and a key characteristic of matching markets is that this is not a valid move. Roth has many cute summaries:

Matching is economist-speak for how we get the many things we choose in life that also must choose us.

I'm sure he enjoys his wordplay too:

The economic world is just as full of surprising detail as the natural world, and markets also often arise by a kind of evolution, by trial and error, without any intelligent design. But markets can also be designed, sometimes from scratch but often after trial and error leads to a market failure.

Mostly this is the greatest hits of his professional career. He characterizes market failure with lots of examples. They can be:

  • Too thin, with not enough buyers or sellers;
  • Congested, which is to say that deals should be struck once sufficient information exchange has taken place; and
  • Unsafe, where the participants are discouraged from honestly revealing their preferences, and hence engage in oftentimes complex and expensive strategic behaviour.

For the design of matching markets, he pushes the classic deferred acceptance algorithm, which involves a central clearinghouse that essentially resolves the preferences of the two distinct kinds of participants in one go. (All preferences are submitted ahead of time, so it does not involve any price discovery.) In contrast a buyer in a financial market is often simultaneously a seller, and the recent attempts in the U.S. to make these more efficient by introducing competing venues is heading in the opposite direction. Similarly the latter encourage dark pools and other off-market mechanisms that leave the public market as the relatively toxic (unsafe) venue of last resort. The resulting regulatory framework is well-intentioned but not theoretically grounded. Roth's off-the-cuff suggestion here is auctions at one-second frequencies, to curtail the HFT arms race.

There is some discussion of repugnant markets, which is expected as he spent quite a bit of time discussing how kidney transplants could be made more efficient while remaining the gift of donors. Again, more wordplay:

To return to the question of kidney sales, virtually no one objects to kidney donation for transplantation. But many people clearly regard monetary compensation for organ donation as a very bad idea, maybe even the kind of bad idea that only bad people have.

... and Roth makes many references to Iran being the only place on Earth where kidneys can be bought and sold (in 2014). There is also an attempt to rehabilitate Hayek by quoting more of him, as is often done for Adam Smith.

Auctions are held up as having similar properties as the deferred acceptance algorithm. I wanted more formal details. It strikes me that the spectrum auctions are so complex that the bidders have to do serious computation between bids, which makes the timing between rounds critical to the fairness of the result. I hadn't heard of the rural hospitals theorem before, but seeing it makes it clear why those hospitals are unlikely to get as many young doctors as they'd like despite the magic of the centralized clearinghouse. Also I'd like to hear more about Islamic finance; taking an equity stake in a home is quite different from simply loaning the money for the house.

Many of my initial impressions — that even a Nobel prize could not satisfy this ego — were eventually put to rest, especially by the extensive notes that make up the final quarter of the book. Roth writes lucidly and anyone disappointed by the lack of technical depth here should certainly pick up his classic from 1990: Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis with Marilda Sotomayor, which tells many of the same stories. My original interest was in phrasing deductive liveness arguments, and I had hoped that showing the termination of the deferred acceptance algorithm was curly, but I fear it is not. I was also wondering how it relates to Arrow's Theorem.