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Hierarchical Cont-Bouchaud Model

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Paluch R., Suchecki K., Hołyst J.

Acta Physica Polonica A

2015

vol. 127

issue 3A

A-108-A-112

We extend the well-known Cont-Bouchaud model to include a hierarchical topology of agent's interactions. The influence of hierarchy on system dynamics is investigated by two models. The first one is based on a multi-level, nested Erdős-Rényi random graph and individual decisions by agents according to Potts dynamics. This approach does not lead to a broad return distribution outside a parameter regime close to the original Cont-Bouchaud model. In the second model we introduce a limited hierarchical Erdős-Rényi graph, where merging of clusters at a level h+1 involves only clusters that have merged at the previous level h and we use the original Cont-Bouchaud agent dynamics on resulting clusters. The second model leads to a heavy-tail distribution of cluster sizes and relative price changes in a wide range of connection densities, not only close to the percolation threshold.

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1 Acta Physica Polonica A

1 2015

1 Hołyst J.

1 Paluch R.

1 Suchecki K.

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Hierarchical Cont-Bouchaud Model