Low-Dimensional Dynamics in Agent-Based Models

摘要

Within recent years, agent-based models have achieved growing prominence in several fields of study. Although powerful and expressive for characterizing the evolution of large populations exhibiting persistent interactions between individuals and high heterogeneity, agent-based methods do not come without tradeoffs. Such methods are burdened by relatively high runtime, lack a formal canonical, declarative, and transparent mathematical semantics, and are often challenging to program, understand, calibrate, generalize and validate. It is therefore important to help modelers recognize modeling contexts requiring the full generality of such models. This paper takes a preliminary step in that direction. Specifically, we built and apply a framework that applies the theory of delay embedding and generic algorithms for intrinsic dimensionality assessment in order to estimate the intrinsic dimensionality of the trajectory of agent-based models. This dimensionality provides a lower bound on the number of state variables required in any model that seeks to reproduce the behavior of these agent based models. Although results are tentative and particularly sensitive to noise, our work appears to indicate that many highly descriptively complex agent-based models may give rise to exceptionally low dimensional global behavior. We suggest that there may be opportunities for expressing the behavior of many complex agent-based models using state equation models offering much far smaller size and greater computational economy.