A_p>0$) or losses ($\Delta A_p<0$), is found to be proportional to the current share as $$|\Delta A_p (t)| \simeq c A_p(t)
\label{eq:DApAp}$$ with $c\simeq 0.1$ \[Fig. \[fig:empirical\] (c)\]. For $A$ so small as $A\lesssim 10^{-5}$, the gain of product share shows fluctuations. The linear scaling in Eq. (\[eq:DApAp\]) appears also in other economic time series [@gibrat1931inegalites; @mantegna1995scaling]. Considering $A_p(t)$ as approximating the time average $\langle A_p\rangle$ of $p$ in the period between $t$ and $t+1$ and $\Delta A_p(t)$ as the standard deviation $\sigma_p$ in the same period, we find Eq. (\[eq:DApAp\]) represent the fluctuation scaling $\sigma_p \sim \langle A_p\rangle^\alpha$ with $\alpha=1$, which has been investigated for diverse complex systems [@menezes04a; @eisler08; @PhysRevE.83.066115] under such names as Gibrat’s law [@gibrat1931inegalites] or Taylor’s law [@TAYLOR:1961aa]. Though simple, Eq. (\[eq:DApAp\]) has far-reaching implications for the underlying dynamics of capital invested for product categories, which we address in the next sections.

Urn model {#sec:model}
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Differentiated evolution of individual product share arise from a huge number of microscopic changes of investment made by companies and countries, which can be modeled as independent trajectories subject to non-gaussian stochasticity [@mantegna1995scaling] or as emerging from exchange between individuals [@yakovenko2009colloquium; @bouchaud2000wealth]. We take the latter approach to understand 