Compartment Models for Innovation and Imitation

This paper introduces a compartmental modeling framework for analyzing the dynamic interplay between innovation and imitation in socio-technical systems. Drawing inspiration from epidemiological models, we represent agents as belonging to distinct behavioral states, such as aspiring innovators, successful inventors, idle imitators, and successful imitators, and model transitions between these states using a system of differential equations. We investigate how varying the fraction of innovators within a fixed population affects system-wide social utility over time. Simulations conducted in Berkeley Madonna reveal that, contrary to common intuition, higher proportions of innovators do not necessarily lead to higher social utility in the short run due to front-loaded opportunity costs. In the long run, however, utility is maximized not when innovation is maximized, but when there is a modest surplus of innovators relative to imitators. We further extend the model to incorporate a baseline productivity class of agents contributing constant social value, allowing for a more realistic assessment of marginal utility. These findings offer insight into the design of balanced innovation policies and provide a flexible foundation for future empirical and agent-based research.