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Percentage of active users in the Internet 2.0 is tiny. Fractions go from * only 1% of Wikipedia's users contribute to making it better * only 0.1% of users upload their own videos to Youtube * only 3% of people with weblogs post on a daily basis * only 1% of Amazon.com customers contribute with reviews The numbers are tiny. But not uncommon. Typical return rates of marketing campaigns or surveys are around 2-5% (see report by the Direct Marketing Association). ...

A wonderful quote about the nature of Game Theory Game theory is no doubt wonderful for telling stories. However, it flunks the main test of any scientific theory: The ability to make empirically testable predictions. In most real-life situations, many different outcomes -- from full cooperation to near-disastrous conflict -- are consistent with the game-theory version of rationality.  by Michael Mandel, on Kahneman and Smith 2002 Nobel Prize in Economics. ...

November was a rather sad month in the world of stochastic differential equations. In the 26th we were suppose to be celebrating the birth of one of the best mathematicians in history, Norbert Wiener, who gives name to the Wiener process, usually denoted W(t). However, in the 10th, Kiyoshi Itô, the father of stochastic differential equations, passed away. Interestingly both are present in a simple stochastic differential equation like this ...

While the individual man is an insoluble puzzle, in the aggregate he becomes a mathematical certainty. You can, for example, never foretell what any one man will do, but you can say with precision what an average number will be up to. Individuals vary, but percentages remain constant. So says the statistician Sherlock Holmes in “The Sign of Four”. Via Gaussianos

A picture is worth a thousand lines of equations By James Robert Brown

Authors: Fabrizio Lillo, Esteban Moro, Gabriella Vaglica y Rosario Mantegna Journal: New Journal of Physics 10 (2008) 043019 LINK arXiv Abstract: Agent-based models of financial markets usually make assumptions about agent’s preferred stylized strategies. Empirical validations of these assumptions have not been performed so far on a full-market scale. Here we present a comprehensive study of the resulting strategies followed by the firms which are members of the Spanish Stock Exchange. ...