...P

nagel@inf.ethz.ch. ETH Zentrum IFW B27.1, 8092 Zürich, Switzerland

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...

martin.shubik@yale.edu

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...

paczuski@alf.nbi.dk

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...

bak@alf.nbi.dk

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....

In this paper, we will also use $N(s) = s \, n(s)$ for the cluster size distribution in logarithmic bins, in particular for the figures.

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... size.

An establishment is ``a single physical location at which business is conducted. It is not necessarily identical with a company or enterprise, which may consist of one establishment or more.'' [12].

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... here.

Remember again, that slopes from log-log plots in logarithmic bins are different by one from the exponent in the distribution. So $n(s) \sim s^{-2}$ corresponds to a slope $-1$ both in the accumulated distribution $n(>\!s)$ and when plotting logarithmic bins $N(s)/N(1)$.

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...fig:non-spatial-gpl).

Note that the approach in this section corresponds to measuring the cluster size distribution every time we give an agent back to the system, while in the simulations we measured the cluster size distribution only just before a cluster was picked for deletion. In how far this is important is an open question; preliminary simulation results indicate that it is important for the spatial case with injection but not important for the non-spatial case in this section.

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... business.

In this model no accumulation of assets is allowed. This simplification will be relaxed in future work.

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... shop.

The simplification that customers react to price changes only is useful because it leads to the separation of time scales between consumer behavior and firm behavior.

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... customer.

If all prices in the system are more than $\delta$ below one, then the model is not well-defined. In the limit of large systems and when starting with prices above one, such a state cannot be reached via the dynamics. - Also note that if the model allowed credit, the exit of such a company would be delayed, allowing losses for limited periods of time.

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... model.

Furthermore, models such as the ones discussed in this paper often have a so-called upper critical dimension, where some aspects of the model become the same as in infinite dimensions. This upper critical dimension often is rather low (below 10).

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