Self-organized criticality in a network of economic agents with finite consumption

We introduce a minimal agent model to explain the emergence of heavy-tailed return distributions as a result of self-organized criticality. The model assumes that agents trade their economic outputs with each other composing a complex network of agents and connections. Further, the incoming degree of an agent is proportional to the demand on its goods, while its outgoing degree is proportional to the supply. The model considers a collection of economic agents which are attracted to establish connections among them to make an exchange at a price formed by supply and demand. With our model we are able to reproduce the evolution of the return of macroscopic quantities (indices) and to correctly retrieve the non-trivial exponent value characterizing the amplitude of drops in several indices in financial markets, relating it to the underlying topology of connections. The distribution of drops in empirical data is obtained by counting the number of successive time-steps for which a decrease in the index value is observed. All eight financial indexes show an exponent m ∼ 5 / 2 . Finally, we present mean-field calculations of the critical exponents, and of the scaling relation m = 3 2 γ − 1 between the exponent m for the distribution of drops and the topological exponent γ for the degree distribution.