JCA HomeIssue Contents

Multilayer Cellular Automata on a Graph Applied to the Exchanges of Cash and Goods
Ranaivo M. Razakanirina and Bastien Chopard

This paper investigates the behaviors and the properties of a “Give and Take” model using multilayer 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 submarkets. 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.

Keywords: Complex system, multilayer cellular automata on a graph, complex network, strongly connected components, economical model.

Full Text (IP)