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Boolean delay equations on networks: An application to economic damage propagation

  • B. Coluzzi
  • M. Ghil
  • S. Hallegatte
  • G. Weisbuch

We introduce economic models based on Boolean Delay Equations: this formalism makes easier to take into account the complexity of the interactions between firms and is particularly appropriate for studying the propagation of an initial damage due to a catastrophe. Here we concentrate on simple cases, which allow to understand the effects of multiple concurrent production paths as well as the presence of stochasticity in the path time lengths or in the network structure. In absence of flexibility, the shortening of production of a single firm in an isolated network with multiple connections usually ends up by attaining a finite fraction of the firms or the whole economy, whereas the interactions with the outside allow a partial recovering of the activity, giving rise to periodic solutions with waves of damage which propagate across the structure. The damage propagation speed is strongly dependent upon the topology. The existence of multiple concurrent production paths does not necessarily imply a slowing down of the propagation, which can be as fast as the shortest path.

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File URL: http://arxiv.org/pdf/1003.0793
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Paper provided by arXiv.org in its series Papers with number 1003.0793.

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Date of creation: Mar 2010
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Handle: RePEc:arx:papers:1003.0793
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  1. Peter Bak & Kan Chen & Jose Scheinkman & Michael Woodford, 1992. "Aggregate Fluctuations from Independent Sectoral Shocks: Self-Organized Criticality in a Model of Production and Inventory Dynamics," NBER Working Papers 4241, National Bureau of Economic Research, Inc.
  2. Sungbin Cho & Peter Gordon & James E. Moore II & Harry W. Richardson & Masanobu Shinozuka & Stephanie Chang, 2001. "Integrating Transportation Network and Regional Economic Models to Estimate the Costs of a Large Urban Earthquake," Journal of Regional Science, Wiley Blackwell, vol. 41(1), pages 39-65.
  3. Gatti, Domenico Delli & Guilmi, Corrado Di & Gaffeo, Edoardo & Giulioni, Gianfranco & Gallegati, Mauro & Palestrini, Antonio, 2005. "A new approach to business fluctuations: heterogeneous interacting agents, scaling laws and financial fragility," Journal of Economic Behavior & Organization, Elsevier, vol. 56(4), pages 489-512, April.
  4. Adam Rose & Shu-Yi Liao, 2005. "Modeling Regional Economic Resilience to Disasters: A Computable General Equilibrium Analysis of Water Service Disruptions," Journal of Regional Science, Wiley Blackwell, vol. 45(1), pages 75-112.
  5. Weisbuch, Gérard & Battiston, Stefano, 2007. "From production networks to geographical economics," Journal of Economic Behavior & Organization, Elsevier, vol. 64(3-4), pages 448-469.
  6. Stéphane Hallegatte & Fanny Henriet, 2008. "Assessing the Consequences of Natural Disasters on Production Networks: A Disaggregated Approach," Working Papers 2008.100, Fondazione Eni Enrico Mattei.
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