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New York Times puzzle is pure game theory

The Upshot is a column in the New York Times based around analytics, data and graphics. (It was conceived around the time when Nate Silver left to work for ESPN). Earlier this week, managing editor David Leonhardt and data journalist Kevin Quealy posted an interesting puzzle, entitled ‘Are You Smarter Than 49,485 other New York Times Readers?’

The puzzle consists of a simple question – you need to pick a number between 0 and 100, and all 49,485 of the responses will be collated (assuming that every single one of the Times’ readership actually enters a number) and averaged. If your guess turns out to be the closest whole number to two-thirds of the average guess, you are clever and you win.

Applied game theory: Students boycott exam and all get an A

A piece on the New York Times Economix blog casts a story from Inside Higher Ed as a piece of applied game theory. Professor Peter Fröhlich of Johns Hopkins University has a grading system in which

each class’s highest grade on the final counts as an A, with all other scores adjusted accordingly. So if a midterm is worth 40 points, and the highest actual score is 36 points, “that person gets 100 percent and everybody else gets a percentage relative to it,” said Fröhlich.

Can you spot the problem? The Economix posts points out that this allows “at least two Bayesian Nash equilibria”:

Equilibrium #1 is that no one takes the test, and equilibrium #2 is that everyone takes the test. Both equilibria depend on what all the students believe their peers will do.

In equilibrium #1, everyone scores the same mark – zero – and the calibrated marking scheme maps this onto 100%. The students, realising this, arranged a complete boycott and were all awarded grade A.

Alas, this was not a game theory class! Prof Fröhlich has since changed his grading scheme.

Further information:

Dangerous Curves (Inside Higher Ed) has some detail of how the boycott was arranged (had just one taken the test, all would have been forced to follow suit).

Gaming the System (Economix) discusses the related game theory and economics concepts.

Steven Strogatz series on “what math can reveal about us and our world”

Steven Strogatz has begun a six-part series in a New York Times blog. ‘Me, Myself and Math’ apparently “looks at us through the lens of math”. Steven explains that this will focus on

how the subject I love — math — relates to the subject we all love — ourselves.
From the DNA that encodes us, to the fingerprints that characterize us, to our place in the universe and our friend counts on Facebook, we are mathematical marvels. In the coming weeks we’ll see what math can reveal about us and our world, and at the same time, how the wonders of us have inspired advances in math.

The first outing, ‘Singular Sensations‘, discusses the topology in patterns on the body like hair and fingerprints.

Source: Me, Myself and Math.