Using Cellular Automata on a Graph to Model the Exchanges of Cash and Goods

  • Ranaivo Mahaleo Razakanirina
  • Bastien Chopard
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6350)


This paper investigates the behaviors and the properties of a “Give and Take” cellular automaton on a graph. Using an economical metaphor, this model implements the exchange of cash against goods, among the nodes of a graph G, with a local pricing mechanism. During the time evolution of this model, the strongly connected components (SCC) emerge, mimicking the creation of independent sub-markets. In the steady state, each SCC is characterized by a unique price obeying the supply and demand law for that sub-market. We also show that the distributions of cash and goods are proportional to the indegree of the cells, reproducing a Zipf’s law of wealth distribution in case of a scale-free graph topology.


Cellular Automaton Random Graph Unit Price Graph Topology Wealth Distribution 
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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Ranaivo Mahaleo Razakanirina
    • 1
  • Bastien Chopard
    • 1
  1. 1.University of GenevaSwitzerland

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