Self-organized criticality in evolutionary systems with local interaction

This paper studies a stylized model of local interaction where agents choose from an ever increasing set of vertically ranked actions, e.g. technologies. The driving forces of the model are infrequent upward shifts ("updates"), followed by a rapid process of local imitation ('diffusion'). Our main focus is on the long-run regularities displayed by the long-run distribution of diffusion waves and their implication on the performance of the system. By integrating analytical techniques and numerical simulations, we come to the following two main conclusions: (1) When the penalty for 'technological dis-coordination' (the single key parameter of the model) is high enough, the system behaves critically, in the sense customarily used in physics -that is, diffusion waves have their size (or reach) distributed according to power laws. (2) If the performance of the system is evaluated by how fast or cost-efficiently it attains any given technological level, the optimal configuration obtains (in parameter space) close to the frontier of the critical region. There, the system no longer displays synchronized behavior but starts to exhibit persistent and critical long-run heterogeneities. In the heuristic language used by Kauffman (1993), the above two conclusions may be interpreted as an indication that (performance-sensitive) evolutionary forces induce the system to be placed 'at the edge of order and chaos'.