Size invariance sector for an agent-based innovation diffusion model

TL;DR

This paper demonstrates that under specific conditions, an agent-based innovation diffusion model on small-world networks exhibits size invariance in saturation time and adoption curve shape, simplifying analysis of large complex systems.

Contribution

It introduces a size invariance sector in an agent-based diffusion model, showing certain results are independent of system size within small-world networks.

Findings

Saturation time is invariant to system size.

Adoption curve shape remains consistent across different system sizes.

Size invariance applies to a subfamily of small-world networks.

Abstract

It is shown that under certain conditions it is possible to model a complex system in a way that leads to results that do not depend on system size. As an example of complex system an innovation diffusion model is considered. In that model a set of individuals (the agents), which are interconnected, must decide if adopt or not an innovation. The agents are connected in a member of the networks family known as small worlds networks (SWN). It is found that for a subfamily of the SWN the saturation time and the form of the adoption curve are invariants respect to the change in the size of the system.