Monday, October 15, 2012

A Prize for Matching

Alvin Roth and Lloyd Shapley won the Nobel Prize today  "for the theory of stable allocations and the practice of market design." This is basically a prize validating non-transferable utility matching.

Roth and Shapley have written many articles establishing many new ideas in the field. Here is one seven-page paper that practically began the field of matching by Gale and Shapley: "College Admissions and the Stability of Marriage." Gale is no longer alive, so he was not eligible for the big prize today. What's amazing about this paper is how readable it is (especially considering the paper was published in a math journal!). The paper not only touches on interesting economics applications like the marriage market and the college admissions process (and explaining stability), but at the end the authors give a few thoughts on mathematics and teaching math. In the conclusion they ask, "What then... is mathematics?" and argue that their article is a great example of mathematical thinking that isn't "numerical or geometrical....The argument is not carried out in mathematical symbols, but ordinary English." Of course, history has shown that the paper is not just mathematics -- it's economics!

Here is Marginal Revolution's write-up on matching and market design.

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