Hierarchical Cont-Bouchaud Model |

R. Paluch
^{a}, K. Suchecki^{ a} and J.A. Hołyst^{a,b}^{a}Center of Excellence for Complex Systems Research, Faculty of Physics, Warsaw University of Technology, Koszykowa 75, PL-00662 Warsaw, Poland
^{b}ITMO University, 19, Kronverkskiy av., 197101 Saint Petersburg, Russia |

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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. |

DOI: 10.12693/APhysPolA.127.A-108 PACS numbers: 89.65.-s, 89.65.Gh, 89.75.-k, 05.40.-a |