The Adjusted R-Square versus <i>k/N</i> and slope versus <i>k/N</i> for the linear fits in <b>Figure 8</b>.

<p>The Adjusted R-Square versus <i>k/N</i> and slope versus <i>k/N</i> for the linear fits in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0058270#pone-0058270-g008" target="_blank"><b>Figure 8</b></a>.</p

The friend number’s effects on the average successful trading ratio, market clustering degree and simple social entropy.

<p>With an increase in the number of friends per agent <i>k/N</i>, this model shifts from no information sharing to more information sharing. This figure shows that as <i>k/N</i> increases from 0 to 0.99, the averages of the successful trading ratio <i>D_t</i> and the degree of clustering <i>C_t</i> increase, and the average simple social entropy <i>E_t</i> decreases. The error bars are also shown. All of the averages are calculated after the first 10,000 time-steps.</p

Sensitivity analysis of the Adjusted R-Square versus <i>R_c</i> for some typical <i>k/N</i> values.

<p>There are only two dots (<i>k/N</i> = 0.10, <i>R_c</i> = 4), (<i>k/N</i> = 0.20, <i>R_c</i> = 2) that are below 0.90, which means that the results obtained from the distribution are quite robust to the variation of <i>R_c</i> values, especially when there is no information sharing (<i>k/N</i> = 0) or the extent of information sharing is high (<i>k/N</i> = 0.60, 0.90).</p

Evolution in the successful trade ratio associated with the degree of information sharing.

<p>This figure shows the 200-iteration moving average of the successful trade ratio. From bottom to top, light gray (<i>k/N</i> = 0), gray (<i>k/N</i> = 0.10) and black (<i>k/N</i> = 0.99) correspond to typical cases from no information sharing to the greatest degree of information sharing, respectively. The average successful trade ratios <i>D_{t_avg}</i> associated with the three cases are 0.45, 0.52 and 0.61, respectively. In this model, more information promotes more successful trades. All of the averages are calculated after the first 10,000 time-steps.</p

Market spatial structures resulting from the degree of information sharing.

<p>Each plot is a spatial distribution of the agents on the two-dimensional <i>L×L</i> lattice. Panel (A) with <i>k/N</i> = 0 represents no information sharing, panel (B) has <i>k/N</i> = 0.10 and panel (C) has <i>k/N</i> = 0.99. The agents scatter on the lattice without agglomeration in Panel (A). The distribution of the agents in Panel (B) appears to be less scattered than that in Panel (A), and several small clusters were observed. Only in Panel (C) can we observe the agglomeration of the agents into obvious clusters. This finding shows that the more information sharing there is, the more likely it is that economic centers will form.</p

Evolution in the degree of clustering associated with the degree of information sharing.

<p>This figure shows the 200-iteration moving average of the degree of clustering. From bottom to top, light gray (<i>k/N</i> = 0), gray (<i>k/N</i> = 0.10) and black (<i>k/N</i> = 0.99) correspond to typical cases from no information sharing to the most information sharing, respectively. The average degrees of clustering <i>C_{t_avg}</i> for the three cases are 3.29, 6.35 and 12.52, respectively. The agents in the pheromone-like mechanism show a much tighter integration than in the other two. All of the averages are calculated after the first 10,000 time-steps.</p

The linear fit in the log-linear scale for <i>k/N</i> = 0, 0.10.

<p>This figure shows the log-linear plot of market size distribution and linear fit for <i>k/N</i> = 0, 0.10. The linear fits have an Adjusted R-Square greater than 0.90, which means that the market size distributions for these two <i>k/N</i> ratios are exponential.</p

The parameters of the model.

<p>The parameters of the model.</p

The symbols used in the unified model.

<p>The symbols used in the unified model.</p

The effects of the random walk probability on the degree of clustering and the market number.

<p>This figure shows that the larger the value of <i>P</i>, the smaller the degree of clustering <i>C_t</i> and the lower the market number. In this model, we set <i>P</i> = 0.10 because <i>P</i> = 0.10 leads the model to produce interesting results, i.e., clustering. The fact that agglomeration does not happen for other values is also a valid and meaningful result.</p