Nobel update: more on Shapley

October 15, 2012

Lloyd Shapley is a mathematical theorist, which means his work isn’t easily conveyed in user-friendly soundbites.  It has nevertheless had a strong influence on a number of practical issues, many of them evident in Al Roth’s work.  What follows is what I learned from my colleague Ignacio Esponda.  (If you’ve seen Broadcast News, you’ll imagine him thinking to himself:  “I say it here, and it comes out there.”)

The prevailing framework of economics has been supply and demand, in which people interact in markets.  Over the last few decades that’s been superseded, in many applications, by game theory, in which people interact in more general settings governed by a set of more or less arbitrary rules that we refer to as a game.  That leads to some basic questions:  What are the likely outcomes of a given set of rules?  What rules lead to the best outcomes?  What kinds of rules produce the same outcomes as supply and demand?  What happens if groups of people can block outcomes they don’t like?

Lloyd Shapley has been making fundamental contributions to game theory since the 1950s.  The American Economic Association describes his work here.  The work described in the Nobel Prize announcement concerns matching games:  games in which we match one group of people with another.  You might think of school choice (matching schools and students), organ transplants (donors and recipients), medical residents (jobs and applicants), and maybe even marriage.  For a variety of reasons we don’t usually solve these problems with markets, but we can look at the pros and cons of other mechanisms.  Shapley’s work with David Gale laid the foundations for theoretical work on these matching games and made possible the growing body of applied work we now call market design.

If you’d like more on this topic, see Alex Tabarrok’s summary.  Or this wonderful link (added Oct 22).

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