Category: game theory

The Ninth Annual Year in Ideas

2009 Year In Ideas

The NY Times Magazine annually publishes its The Year in Ideas issue, devoted entirely to “the most clever, important, silly and just plain weird innovations … from all corners of the thinking world.” A surprising number of these ideas are based on a study or research article or something similar that employs some bit of mathematical and/or statistical analysis. The ones I’ve listed below are chosen as being the ones that most prominently feature mathematics ideas, or feature mathematics and/or mathematicians centrally. Listed alphabetically:

  • Black Quarterbacks Are Underpaid by Jason Zengerle describes the statistical analysis of two economists, David J. Berri and Rob Simmons, who discovered that in the NFL black quarterbacks are typically paid much less than white quarterbacks. Their analysis goes farther, however, and notes that the apparent cause is not necessarily racism. Instead, the NFL quarterback rating statistic is the culprit. NFL contracts are often based on hitting certain statistical levels, and for quarterbacks the statistic used is often the QB rating. Since QB rating fails to count rushing yards at all–something that black quarterbacks typically excel at–black quarterbacks are typically ‘discounted’, QB rating-wise.
  • Forensic Polling Analysis visits a topic seen already here in this blog: the suspicious polling numbers of the polling firm Strategic Vision LLC. You can visit that entry or the Times article for more info.
  • In a blow to meritocracy-lovers everywhere, another entry notes that Random Promotions, rather than merit-based ones, can actually produce better businesses (and typically do, at least in simulations). The article by Clive Thompson describes a study done by a trio of Italian scientists in which the researchers created a virtual 160-person company and then tried out various different promotion schemes within the company, with the aim of seeing which scheme improved the company’s productivity the most. Promoting on merit turned out to be a lousy idea (at least for the company as a whole) while promoting at random turned out to be the top strategy. In the middle was the curious idea of alternately promoting the best and then the worst employees. The fact that the mixed best/worst strategy outperformed the merit strategy is yet another example of Parrando’s Paradox, a phenomenon first identified by game theory.
  • Massively Collaborative Mathematics features the first mathematical theorem proved by a ‘collective mind’, if you will. In January 2009, Timothy Gowers, one of the top mathematicians in the field, proposed on his blog that the mathematical community, as a whole–or at least that portion that knew and read his blog–attack a long-standing unsolved problem in mathematics known as the Density Hales-Jewett Theorem. Contributors ranged from eminent mathematicians to high school teachers, and hundreds of thousands of words worth of ideas were eventually proposed, developed, discarded, combined, and so forth. Gowers had initially set the bar low, hoping this ‘Polymath’ project would result in “anything that could count as genuine progress toward an understanding of the problem.” Instead, six weeks later the problem was completely solved. A paper detailing the result, authored by D.H.J. Polymath, has been submitted to a leading journal.
  • Finally, the (alphabetically) last idea listed, “Zombie-Attack Science,” features a story that appeared on this blog previously. See that entry, or the Times article, of course, for details.

The Predictioneer’s Game

We’ve seen Bruce Bueno de Mesquita here on this blog before for his work using game theory to predict political events. Now he’s written a book, The Predictioneer’s Game: Using the Logic of Brazen Self-Interest to See and Shape the Future. The book has garnered pretty good reviews from the in the NY Times and Boston Globe, among others, although most reviews admit to being uneasy with the idea that human behavior could ever be predictable to the degree claimed by the author. Which is understandable, especially since one of Bueno de Mesquita’s bedrock axioms is that those humans are behaving selfishly, or at least `looking out for number one’ with any number two a distant afterthought. (The book’s subtitle: Using the Logic of Brazen Self-Interest to See and Shape the Future.)

Whatever your reaction, Bueno de Mesquita’s approach seems to work: the book documents successful predictions of all sorts of things, from naming the successor to Iran’s Ayatollah Khomeni to foretelling the downfall of Pakistan’s Pervez Musharaff. The author has also been retained on a number of occasions by large corporations to weigh in on their decision-making, and the book sports recommendations from former Nobel laureates, a former CIA director and a former Secretary of State. And Bueno de Mesuita was recently bestowed an even higher honor: he was interviewed on the Daily Show.

Darwin Plays Game Theory—and Wins


Game theory is a branch of mathematics that explores how people (or entities made up of people, like organizations) make decisions. This article from Discover magazine shows one of the first instances of game theory being applied to animal behavior. The animals in question are ravens, and in 2002 Sasha Dall, a mathematical ecologist at the University of Exeter in England, used game theory to explain why young ravens scout for carrion by themselves but then recruit other birds to join the feast.

Even more impressively, Dall’s model predicted that ravens would likely employ another strategy, one that had never been observed in ravens: gang foraging, where a large group of birds scavenge together. The article describes what happened when scientists looked to see if Dall was correct:

Behavioral ecologist Jonathan Wright of the Norwegian University of Science and Technology discovered this very behavior in the field. He tracked ravens in North Wales by implanting carcasses with different-colored beads that the birds ingested and later coughed up. Analysis of the beads indicated that ravens in some roosts were searching, eating, and benefiting together, just as Dall anticipated.

Can Game Theory Predict When Iran Will Get the Bomb?

This Aug. 12, 2009 NY Times article (free registration required) by Clive Thompson features the work of Bruce Bueno de Mesquita, a professor at New York University who has been using game theory to forecast political events and decisions over the past 30 years. Also see Bueno de Mesquita’s TED talk here and his interview on NPR.

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