Wolfram Science

Fiona Maclachlan: The Distribution of Market Shares in Monopolistically Competitive Markets

Monopolistically competitive markets are much more common in the real world than perfect markets, but perfect markets are the usual assumption in theoretical economics, mainly because they are more tractable from a mathematical perspective. However, there are many empirically observed distributions that lack a formal model that describes them, and thus tend to receive less attention from the economics community. One notable example was the observation that the distribution of intervals between random points corresponded to the market share distribution of the top 4 auto companies in 1967.

Other distributions obeyed the so-called broken stick rule: world religions, price patterns. However, there has been no theoretical model in which to fit the empirical result. More recently, stochastic proportional growth models were proposed for these, but not without problems: distributions are not perfectly log-log, but rather more like power-log on one end, and exponential on the other. One problem with the stochastic proportional growth model is that it relies on a so-called preferential attachment model. But this is not always the case in reality. This raises the question of what kind of distribution would arise in a market without preferential attachment.

Fiona offers one such model: assume uniform distribution of consumers over a given parameter, for instance, "sweetness" for a soft drink. Firms select their "sweetness" parameter at random. One can then (assuming a given distribution of tastes among consumers), assume that consumers will make their choices based on which products lie closest to their preference.

The distributions achieved through explicit simulation of the model that are more consistent with empirical observations than the Pareto distribution. The idea in Fiona's talk is similar to the discussion of Zipf's law (NKS 1014): a simple model using randomness could be the actual underlying generator of this and other phenomena that exhibit power law behavior.

Jason Cawley "NKS Time Series"

I stepped into this talk half-way through, so I think I missed the key points, but it was interesting.

The NKS book included a single model for market behaviour (rule 90 if I remember), and in this talk Jason Cawley presented a large number of experiments that show further evidence of the relevance of simple programs to explaining time series behaviour of market and economic data.

One point he made was that the models he presented capture some qualitative features of the real world data like "crashing" behaviour at different scales. Another theme was the general goal of NKS model fitting.

He has looked at Markov chain's from an NKS point of view (something not covered much in the book). I think the NKS type behaviour in such systems he shows is quite surprising. He has a novel and interesting analysis of it too.

Cristian Opazo and Anirudh Tiwathia, "Eye-Tracking Study Using Cellular Automata Patterns as Visual Stimuli"

Posted by Kathryn Cramer.

The experimenters examined how viewers looked at NKS images using eye tracking technology. Viewers seem to be using different strategies for looking at NKS images than one would expect from an optimal strategy for extracting maximal information from minimal effort.

After the examples were presented, there ensued a lively discussion of what they eyes of the viewers were trying to do: distinguish figures from ground; detect edges, distinguish faces, etc.

Alan Bachers, "Training the Brain to Enter Class Four Space"

Posted by Kathryn Cramer.

Using neurofeedback technology, Alan Bacher observes that class 4 states have very posetive effects on the human subject: increased central nervous system flexibility, resiliance, etc., whereas class 1, 2, and some class three states tend to be pathalogical.

The general upshot seems to be that the benefits of mental states such as meditation are observable as class 4 states and that problems such as ADD can be treated by using neurofeedback to trend the brain back toward class 4 states.

In March of 2005, at the International Conference on the Fantastic in the Arts, Rudy Rucker described many of the same general ideas, but without the specifics. I asked him after his speech how literally he meant in describing class 4 mental states as meditative. So I asked the presenter whether he and Rudy had talked about this, and as it happened they had, at NKS2004.