I’m glad to see that finally someone is putting mathematics to some good use. I present to you The social norm of leaving the toilet seat down: A game theoretic analysis. (Via Crooked Timber.)
Ariel Rubinstein has made his book, Modeling Bounded Rationality, available online. Economic models tend to assume that humans are mistake-free calculating machines; economists have tried to introduce more realistic assumptions under the banner of bounded rationality. This is a far-from-settled problem, mainly because there are more ways to be wrong than there are to be right.
A sunspot equilibrium is a market equilibrium in which prices depend on otherwise irrelevant random variable. The name is inspired by a theory of nineteenth century economist William Jevons that sunspots affected the stock market. (The theory, while wrong, isn’t quite as rediculous as it sounds. Jevons thought, by looking at the data he had on sunspots and agricultural prices, that he detected a pattern that indicated that sunspots caused crops to fail, which in turn caused recessions.)
A sunspot equilibrium would then be a self-fulfilling prophecy. If everyone expected that sunspots caused recessions, that in principle could be sufficient to cause a recession, even if the cause-and-effect existed entirely in people’s heads. Note that this outcome, while not optimal, would still be individually rational: even if you knew that sunspots didn’t really cause recessions, you would know that everyone else was expecting a recession, so you would act accordingly.
Karl Shell, one of the inventors of the concept, has a list of links to his papers on sunspot equilibria. In particular, he links to a short survey article he co-authored with Bruce Smith.
The University of Liverpool (UK) has a vacancy for a post-doc researcher and for a PhD student, both in automated mechanism design. The expertise we are looking for includes game theory, mechanism design and auction theory, mathematical economics, and computational versions of same. These posts are part of a major UK research project on market-based control of complex computational systems.
The latest issue of the Post-Autistic Economics Review is now out, available here. It has an interesting article by philosopher Donald Gillies arguing against the centrally-organized reviews of university research activities which British academics have had to endure these last 20 years, and which now look likely to be adopted in Australia, NZ and elsewhere. One argument he makes is that one’s peers are usually quite bad at judging the long-run impact and quality of one’s research, especially when the research is innovative, and Gillies gives the example of Frege’s Begriffsschrift, the first axiomatic treatment of propositional and predicate calculus. When this was published in 1879, it was slammed by Frege’s contemporaries, and it was only recognized for the seminal work it is two decades later. If Frege had been working in a British University a hundred years later, both he and his department may have faced termination by his university administration, given the hostility that his own peers felt towards his work; lots of departments have been closed, and academics made unemployed, as a result of the peer assessments of the British Research Assessment Exercise (RAE).
A longer version of Gillies’ paper is available on his web-site, here.
I spotted a survey article, Behavioral Economics: Past, Present, and Future, which gives a guide to this fairly-new field of economics. The subject was born from a mathematical failure. Economists had given precise axioms as to how people would take into account time and uncertainty when making decisions. The axioms allowed precise predictions that (unlike most economics) could be tested in small-scale experiments with a few test subjects. The result was almost-total failure: nearly every prediction turned out to be wrong. Instead of this being the last word on the subject, this has inspired large amounts of research into finding empirical regularities in the discrepancies between the predictions and the experimental results, and formulating a new theory that is both precise and correct. It’s interesting because the original failure could have led to a turn away from mathematical modeling altogether, but it instead has led to research in improved mathematical modeling.
The site Game Theory .net has links to a truly gigantic collection of lecture notes on game theory and its economic applications.
Auctions have provided a real-world arena in which to apply game theory. The theory has actually been applied to design auctions; most famously, the auctions for 3G wireless spectrum were designed along the principles of the theory.
Paul Klemperer has assembled several articles on the subject into a (fairly non-technical) book, and has provided the original articles online. For a more detailed approach, see this survey.
The (sort-of) Nobel Prize in Economics has been announced. The contributions of one of the two, Robert Aumann, are almost purely mathematical work in game theory.
His most interesting idea is that of correlated equilibria. The usual definition of equilibrium in a non-cooperative game, Nash equilibrium, rules out certain kinds of cooperation, even when that cooperation is in the self-interest of each player. Correlated equilibria allow randomized strategies which rely on a random event that is known to both players. Some details about correlated equilibria can be found
here.
(As an aside, the Wikipedia entry for Aumann is unusually bad, so it’s a good candidate for updating, if anyone’s interested. There’s also no entry for correlated equilibrium.)
Mark Blaug has written a hatchet job on Ugly Currents in Modern Economics. One particular development that draws his ire is the increasing mathematization of the field. The article does a good job of summarizing the major trends in the field while explaining why most of them are wrong.